= carpals Volar margin = flexor retinaculum Medial margin = pisiform & hook **of** the hamate Lateral margin scaphoid & **trapezium** Proximal margin = radiocarpal joint Distal margin = MC base Contents: Flexor digitorum/**of** the triangular fibrocartilage (arrowhead) is also present. Diagnosis Kienbocks Disease (avascular necrosis **of** the lunate). Osteonecrosis **of** the lunate Negative ulnar variance Kienbock Lateral – lunate osteonecrosis A few anatomical variants **Examples** from one study: Hypoplasia **of** the hook **of**/

5 seconds © Boardworks Ltd 2005 13 **of** 40 Problems that lead to equations to solve What is the height **of** a **trapezium** with an **area** **of** 40 cm 2 and parallel sides **of** length 7 cm and 9 cm? The formula used to find the **area** A **of** a **trapezium** with parallel sides a and b /Formulae © Boardworks Ltd 2005 26 **of** 40 Formulae where the subject appears twice Sometimes the variable that we are making the subject **of** a formula appears twice. For **example**, S = 2 lw + 2 lh + 2 hw where S is the surface **area** **of** a cuboid, l is its/

its stellar classification identity. Despite its cooler temperature the red giant will be very luminous because **of** its large surface **area**. Red giants will have more solar winds than normal stars which will help dispel more mass/**example** is the Orion Nebula which you can see as the fuzzy patch in the sword part **of** the Orion constellation. It is about 1500 light years away and is 29 light years across. The nebula is lit up by the fluorescence **of** the hydrogen gas around a O-type star in the **Trapezium** cluster **of**/

bones **of** the arm – The humerus – Proximal **area** **of** the limb from the scapula to the elbow Contains the bones **of** the forearm – The radius and ulna Contains the bones **of** the/6-25 Bones **of** the Right Wrist and Hand. ULNA Styloid process **of** ulna Lunate Triquetrum Pisiform Hamate Metacarpal bones RADIUS Styloid process **of** radius Scaphoid **Trapezium** Trapezoid Capitate /9) Some synovial joints have additional padding – In the form **of** menisci – For **example**, in the knee Fat pads can also act as cushions Ligaments /

-5 -8 -9 -8 -5 07 LoS Equation **of** Line **of** symmetry is x = 1 Drawing quadratic graphs **of** the form y = ax 2 + bx + c **Example** 1. Minimum point at (1, -9) Look at graphs **of** some trig functions? sinx + circle 90 o 180 o/ triangle) and angles on a straight line add to 180 o Take 1 identical copy **of** this right-angled triangle and arrange like so. **Area** **of** **trapezium** = ½ (a + b)(a + b) = ½ (a 2 +2ab + b 2 ) **Area** **of** **trapezium** is also equal to the **areas** **of** the 3 right-angled triangles. = ½ ab + ½ ab + ½ c 2 So ½ (a 2/

work out the **area** **of** a rectangle? Which two lines are parallel? Which line is perpendicular to both the red and blue lines? Draw a line which is parallel to the orange line. Give me some **examples** **of** shapes that have pairs **of** parallel lines. Can/it is a kite; a parallelogram; a rhombus; an isosceles **trapezium**? Which quadrilateral with one line **of** symmetry has three acute angles? Education Leeds 20090212 VJC Enlarge 2-D shapes, given a centre **of** enlargement and a positive whole- number scale factor. Step 7d /

. Work out the **area** **of** each part. Add up the separate **areas**. Composite Shapes Split them up. Work out the **area** **of** each part. Add up the separate **areas**. Notes **Area** = **area** **of** triangle + **area** **of** rectangle Saturday, 30 September 2006 ©RSH **Trapezium** (quadrilateral with 2 parallel sides) **Area** = ½ x (a +b) x h **Trapezium** (quadrilateral with 2 parallel sides) **Area** = ½ x (a +b) x h Notes Saturday, 30 September 2006 ©RSH **Example** **Area** = ½ x (a +b/

and present the recent progress in a number **of** **areas** which are important for the Tevatron and LHC –Matching **of** matrix elements and parton showers Traditional Matching /common techniques converge faster –**Trapezium** rule –Simpsons rule However only if the derivatives exist and are finite. Otherwise the convergence **of** the **Trapezium** or Simpsons rule will /the new integration variable. Lets consider the **example** **of** a fixed width Breit- Wigner distribution where –M is the physical mass **of** the particle –m is the off-/

kite we could do the same to get the formula for a **trapezium**: **Area** = Remember the height must be the a and b are the parallel sides. **Area** **of** a **trapezium** PERPENDICULAR height **Example** 3 Find the **area** **of** the following. 32m 71m 320cm 3·7m FIRST get all lengths in metres Only use the lengths **of** the parallel sides and the perpendicular height 26m 22cm 27cm 11cm 25cm/

: i is the x-coord **of** the centroid **of** the **areas** given by the blue **trapezium**, the green **trapeziums** and the black **trapezium** -4.1 -2.5 -ve medium Required i value Centroid **of** three trapezoids Propositional Calculus and Puzzles/ Tautologies evaluate to T in all models. **Examples**: 1) 2) - e Morgan with AND Semantic Tree/Tableau method **of** proving tautology Start with the negation **of** the formula α-formula β-formula α-formula - α - formula - β - formula - α - formula **Example** 2: BC BC Contradictions in all paths /

the **area** **of** a rectangle work out the **area** **of** a parallelogram calculate the **area** **of** shapes made from triangles and rectangles calculate the **area** **of** shapes made from compound shapes made from two or more rectangles, for **example** an L shape or T shape calculate the **area** **of** shapes drawn on a grid calculate the **area** **of** simple shapes work out the surface **area** **of** nets made up **of** rectangles and triangles calculate the **area** **of** a **trapezium**/

plane 7. Width and circumference **of** **Trapezium** A B Width = ½ ( AB + CD). t t Circumference = AB + BC + CD + DA C D **Example**: Find the **trapezium** width in the picture! D E C 8 10 A B 15 Answer: Width = ½ ( AB + CD) CE = = = = Adaptif Hal.: 17 ANGLE AND PLANE Width and circumference **of** flat plane 8. **Area** width side n arranged Side n arranged which has length/

) Velocity (ms –1 ) 20406080100120 2.5 5 7.5 10 0 12.5 140 In this **example**, the **area** under the graph is given by a **trapezium** with height 12.5 and parallel sides **of** length 130 and 90. Displacement = = 1375 m The first part **of** the graph shows an acceleration **of** 0.42 ms –2, the second part 0 and the last part a deceleration/

hh y3y3 y1y1 h y2y2 ab The **Trapezium** rule. Complete the strips to get trapezia. Add up **areas** **of** the form Simpson ’ s Rule We complete the tops **of** the strips as shown with parabolas. y5y5 y4y4 y3y3 y1y1 y2y2 ab x y x0123456 -0.501310 **Example** Rectangle **Trapezium** Simpson Given the following table **of** values, find the approximate value **of** using Simpson’s rule with 8 sub/

**of** polygon that has three sides. **Examples** **of** triangles: Confidential **Area** **of** a Triangle The **area** **of** a triangle is given by "half **of** base times height“. **Area** = where b is the length **of** the base h is the height **of** the triangle. Note: The height is the length **of** a line segment perpendicular to the base **of**/ them is 9 cm. If the **area** **of** the **trapezium** is 315 cm², find the sides. Answer: 20 cm, 50 cm 7. The sum **of** the parallel sides **of** a trapezoid is 0.9 m. If the **area** **of** trapezoid is 360 cm², find the /

figurative language, considering the impact Identify and comment on writer’s use **of** language for effect. For **example**, precisely chosen adjectives, similes and personification. Identify grammatical features used by/ **trapezium** Know what a parallelogram is and describe it in mathematical terms Know what a rhombus is and describe it in mathematical terms Know what a **trapezium**/can name and locate some **of** the main islands that surround the United Kingdom. I can name the **areas** **of** origin **of** the main ethnic groups in /

break all the way through. Diagnose it by placing a tuning fork on the bone, but not at the **area** **of** tenderness…the vibration travels down the shaft **of** the bone until it reaches the fracture site. This will be very painful if it is a stress fracture/ convex in one plane and concave in the other. They fit together like a rider on a saddle. **Examples** are at the base **of** the thumb (between the **trapezium** and metacarpal I). Saddle joints are biaxial joints; in primate anatomy, allows for the opposable thumb Ball and/

antonyms (For **example**, big, little, large) Use **of** the passive voice to affect the presentation **of** information in a/**of** their properties Know the properties **of** rectangles such as parallelogram; **trapezium**; rhombus Know that the total **of** the three angles **of** any triangle adds up to 180˚ Use a protractor to measure individual angles **of** a triangle Draw a triangle given size **of** sides and angle sizes Know that the four angles **of**/ Ltd 201433 Shape and Measures Calculate **area** **of** parallelograms and triangles Data: Draw, /

man. Both the cars are moving w.r.t. a stationary man. Both the cars are at rest w.r.t. each other. In the **examples** **of** motion **of** ball and car, man is considered to be at rest (stationary). But, the man is standing on the Earth and the Earth itself moves around / CB) s = ½ x t x (u + v) s = ½ x t x (u + u + at) s = ½ x (2ut + at 2 ) s = ut + ½ at 2 Third equation **of** motion The **area** **of** **trapezium** OABC gives the distance travelled. s = ½ x OC x (OA + CB) s = ½ x t x (u + v) (v + u) = 2s t From the first equation/

them **Area** & Volume **Area** **of** Shapes **Trapezium** One pair **of** parallel sides Total **area** = bh + ½.ah - ½.bh = ½.bh + ½.ah = h / 2 (a+b) **Area** 1 → b × h h b a 2 1 a - b **Area** 2 → ½ (a – b) × h **Area** **of** a **trapezium** = ½ (a +b) × h = h / 2 (a+b) **Area** & Volume **Area** **of** Shapes Parallelogram **Area** = a × b = length × perp. height a b Kite **Area** = ½ ab = ½ × length × width b a **Area** & Volume **Area** **of** Shapes Find the **area** **of** the/

is not too complicated and the method(s) is representative For instance, AAS test for congruency, Midpoint Theorem, Intercept Theorem, Intersecting Chord Theorem Computation & proof Computations often involve proofs **Example** Given the **trapezium** ABCD with ∠ ABC a right angle. Find the **area** **of** the shaded region. 4cm 10cm 6cm Without using similarity and congruency **of** triangles, what we can do is very limited. Thank you!

:5. The perpendicular distance between them is 9 cm. If the **area** **of** the **trapezium** is 315 cm², find the sides. 7. The sum **of** the parallel sides **of** a trapezoid is 0.9 m. If the **area** **of** trapezoid is 360 cm², find the perpendicular distance between the parallel sides. Your Turn Confidential17 8.The **area** **of** a trapezoid is 210 cm²and its height is 14 cm/

perimeter is 9+9+9+9=36cm **Area** To calculate **area** you need to multiply one side by another. So if a square has a side **of** 9cm you have to do 9x9=81cm/ 5. Factors Factors are numbers you multiply together to get another number. **Example**: 2 and 3 are factors **of** 6, because 2 × 3 = 6. If they only have 2 factors then/ pushed over square and a parallelogram is a rectangle pushed over. **Trapezium** has a pair **of** parallel lines. Kite has two pairs **of** adjacent sides that are equal. Triangles An equilateral triangle has three/

2 m 4.5 m 7 mm 5 mm **Area** = ½ x 7 x 5 = 17.5 mm 2 The **Area** **of** a **Trapezium** **Area** = ½ the sum **of** the parallel sides x the perpendicular height A = ½(a + b)h a b h b ½h a **Area** **of** **trapezium** = **area** **of** parallelogram A = ½(a + b)h A/ cross-sectional **area**. Triangular-based prism Rectangular-based prism Pentagonal-based prism Hexagonal-based prism Octagonal-based prism Circular-based prism Cylinder Cuboid Find the volume **of** the following prisms. Diagrams Not to scale In each **of** the following **examples** the cross-/

2 ) and Ozone (O 3 ) are **examples** **of** allotropes,having different chemical and physical properties. STEP II Table 4.3 Properties **of** allotropes **of** oxygen PropertiesOxygen(O 2 )Ozone (O 3/in summer. In installing this unit, it was ensured that the quality **of** ground in the **area** was not affected. 1. MRL has installed non-chromate type treatment /and generator sets are primarily responsible for polluting the ambient air around the Taj **Trapezium** Zone (TTZ). Both inside and outside, the marble has decayed and yellow /

facial bones and are named according to the specific bones they connect –**Examples**: Frontonasal suture Occipitomastoid suture ANTERIOR SKULL POSTERIOR SKULL Overview **of** Skull Geography The anterior aspect **of** the skull is formed by facial bones, and the remainder is formed /posterior to the ear –Anchoring site for some neck muscles –Full **of** air cavities (mastoid sinuses: air cells) Position adjacent to the middle ear cavity (high-risk **area** for infections spreading from the throat) puts it at risk for /

only be regressed on x 1i in stage (2). **Examples** **of** summary measures include the **Area** Under the Curve (AUC) or the overall mean **of** post-randomisation measures. 15 Summary measures 16 17 **Area** Under the Curve (AUC) 18 Calculation **of** the AUC The **area** can be split into a series **of** shapes called **trapeziums**. The **areas** **of** the separate individual **trapeziums** are calculated and then summed for each patient. Let Y/

2 ) and Ozone (O 3 ) are **examples** **of** allotropes,having different chemical and physical properties. STEP II Table 4.3 Properties **of** allotropes **of** oxygen PropertiesOxygen(O 2 )Ozone (O 3/in summer. In installing this unit, it was ensured that the quality **of** ground in the **area** was not affected. 1. MRL has installed non-chromate type treatment /and generator sets are primarily responsible for polluting the ambient air around the Taj **Trapezium** Zone (TTZ). Both inside and outside, the marble has decayed and yellow /

sitting in that saddle Biaxial –Circumduction allows tip **of** thumb travel in circle –Opposition allows tip **of** thumb to touch tip **of** other fingers **Example** –**trapezium** **of** carpus and metacarpal **of** the thumb Principles **of** Human Anatomy and Physiology, 11e172 TYPES **OF** SYNOVIAL JOINTS In a ball-and-socket joint, the ball-shaped surface **of** one bone fits into the cuplike depression **of** another (Figure 9.10f). Movements are flexion-extension/

5 **of** 6) Saddle joint **Trapezium** Metacarpal bone **of** thumb III II Movement: biaxial **Examples**: First carpometacarpal joint © 2012 Pearson Education, Inc. Figure 9-6 Synovial Joints (Part 6 **of** 6) Ball-and-socket joint Humerus Scapula Movement: triaxial **Examples**: Shoulder/Discs Normal intervertebral disc Slipped disc Compressed **area** **of** spinal nerve Nucleus pulposus **of** herniated disc Spinal nerve Spinal cord Anulus fibrosus T 12 L1L1 L2L2 A lateral view **of** the lumbar region **of** the spinal column, showing a distorted/

scalar is a quantity which has magnitude only. For **example**, displacement, velocity and force are vectors. For **example**, distance, temperature and **area** are scalars. 13.1 Concepts **of** Vectors and Scalar B. Representation **of** a Vector The directed line segment from point X/vectors in terms **of** a and c. (a) (b) Solution: (a) (b) **Example** 13.11T 13.3 Vectors in the Rectangular Coordinate System B. Point **of** Division **Example** 13.11T The figure shows that the **trapezium** ABCD with AB // DC. E is the mid-point **of** AB such /

c.on the abdomen level Be.d below the waist level 65. In a double-contrast barium enema examination, the primary **area** **of** interest for a 45 dergree RAO projection is the: a.rectum b.splenic flexure c.hepatic flexure d.sigmoid colon An/42. Which **of** the following carpal bones is the most frequently fractured? a.hamate b.scaphoid c.**trapezium** d.pisiform The reduction **of** radiation intensity due to scattering and absorption is called ____. A.reflection B.refraction C.attenuation D.dispersion Which **of** the following /

- variable small **area** **of** anesthesia over the dorsum **of** the hand and the dorsal surface **of** the roots **of** the lateral three and/**of** the middle and distal phalanges **of** the same fingers. 43 Joints Joint (articulation, arthrosis): a point **of** contact between two bones The jxn. Between neighboring bones Joint Classifications: (3 types) 1. Fibrous: bone-CT- bone **Examples**/**of** the ulnar nerve Laterally: The radial artery Wrist Joint 60 Carpometacarpal Joint **of** the Thumb Articulation: Between the **trapezium** and the base **of**/

the **area** **of** 2D rectilinear shapes to discover the size **of** various set designs. 5Dance Star Investigating mathematical definitions and descriptions **of** different dance genres. 6 Plotting Physical Theatre Constructing a range **of** loci using a ruler and compass to represent movement or position according to a certain rule. 7 Plotting Physical Theatre Applying construction and loci skills to a range **of** physical theatre and dance **examples**/

up our method. **Area** **of** a **Trapezium** a b h Questions Estimating What do we mean by estimating? Why might we estimate a value? Estimating **area** under curves 10 5 0 1 2 3 A B C Below is the graph **of** y = 10 – x 2 We are interested in finding the **area** under the curve /integration7Trap&taskID=2060 The explanation on page 2 shows us a slightly quicker way. **Example** on page 3 Step by Step 1.Sketch the curve with strips drawn on and x-axis labels. 2.Make a table **of** x and y values. 3.Put the y values into the formula: 4./

. I = 2 1 x 2 dx x 33x 33 2 1 = 2 332 33 = 1 331 33 – 7373 = 8383 1313 – 7373 = **Example** 2: Find the **area** enclosed by the curve y = 3x 2 – 6x and the x axis. Firstly we need to find where the curve crosses the x-axis. 0 = 3x 2 – 6x x/= –x 2 – 4x + 5 dx 5 1 2x dx 5 1 51 x = 1 or 5 Note: The 1 st part **of** the integral 2x dx 5 1 i.e. ( the **area** under the line) could be found by calculating the **area** **of** a **trapezium**. 6x6x 5 1 – x 2 – 5 dx R = 3x23x2 x 33x 33 – – 5x 5 1 = ( /

information given. One to try 6cm 7cm **Area** = 6 x 7 =42 cm2 Triangle **Area** = ½ bh ( ‘h’ is the vertical height) b b **Trapezium** (a quadrilateral with one pair **of** parallel sides) b Add together the parallel sides, divide by 2 and then multiply by the distance between them. **Area** = (a + b) x h 2 **Example** 2cm 10cm 5cm **Area** = (2 + 5) x 10 2 = 3.5/

Rule y x The Mid-ordinate Rule is similar to the **Trapezium** Rule. It uses a series **of** rectangles **of** equal width to estimate the **area** under a graph between two points a and b. The height **of** each rectangle is determined by the height **of** the curve at the m_________________ **of** the interval. hy 1 + hy 2 + hy/ OPTN, F4 (calc), F4 (intergrate) enter X^3,1,5) press EXE 156 The Mid-ordinate Rule **Area** h(y 1 + y 2 + y 3 +... + y n-1 + y n ) x y = f(x) 0.25 **Example** Question 4 1 A /3(0.25 + 1 + 0.25) = 1.57 (2 dp/

2.To show a connection between the SUVAT equations & velocity/time graphs 3.To work through lots more **examples** **of** using the SUVAT equations Book Reference : Pages 112-118 Consider some generalised motion, starting with an initial velocity/**areas**: For the rectangle : **area** = ut For the triangle :**area** = ½ base x height **area** = ½ t (v – u) Total **area** = ut + ½ t (v – u) 2s = 2ut + t(v – u) s = (u + v)t (SUVAT 2) 2 An alternative view: We are actually trying to find the **area** **of** a **trapezium** which is:- Half the sum **of**/

do not change wrt space (position) or time. Velocity and cross-sectional **area** **of** the stream **of** fluid are the same at each cross-section. E.g. flow **of** liquid through a pipe **of** uniform bore running completely full at constant velocity. UiTMSarawak/ FCE/ BCBidaun/ / FCE/ BCBidaun/ ECW301 UiTMSarawak/ FCE/ BCBidaun/ ECW301 **Example** 3.4 (Douglas, 2006) An open channel has a cross section in the form **of** **trapezium** with the bottom width B **of** 4 m and side slopes **of** 1 vertical to 11/2 horizontal. Assuming that the /

work on more challenging mathematics, there are still some who require substantial support. The workshop will explore **examples** **of** tasks with low "floors" but high "ceilings" that allow all students to engage with the tasks/ and **areas** **of** parallelograms, **trapeziums**, rhombuses and kites Investigate the relationship between features **of** circles such as circumference, **area**, radius and diameter. Use formulas to solve problems involving circumference and **area** Develop the formulas for volumes **of** rectangular and/

kite www.mathsrevision.com Parallelogram **Trapezium** Circle Compiled by Mr. Lafferty Maths Dept. **Area** Level 4 Learning Intention Success Criteria We are revising **area** **of** basic shapes. Know formulae. Use formulae correctly. www.mathsrevision.com Show working and appropriate units. 11-Apr-17 Compiled by Mr. Lafferty Maths Dept. **Area** **Example** : Find the **area** **of** the V – shape kite. Level 4 **Example** : Find the **area** **of** the V – shape kite. 4cm/

In the diagram below BE is parallel to CD and all measurements are as shown. (a)Calculate the length CD (b)Calculate the perimeter **of** the **Trapezium** EBCD 4.8 m 6 m 4 m 4.5 m 10 m A C D 8 cm 3 cm 7.5 cm So perimeter /**area** with sides 2 units long. Draw an **area** with sides 4 units long. 2 2 4 4 **Area** **of** Similar Shape 4cm 2cm 12cm 6cm Small **Area** = 4 x 2 = 8cm 2 Large **Area** = 12 x 6 = 72cm 2 Connection ? Another **example** **of** similar **area** ? Work out the **area** **of** each shape and try to link **AREA** and SCALE FACTOR Large **Area**/

able to evaluate an integral to infinity ∞ The **Area** Between A Line and a Curve A kind **example** with give you the points **of** intersection. You have two choices... 1: Find the **area** below the line between x=1 and x=3. Or 1: Find the **area** **of** the **trapezium**/triangle below the line 2: Then find the **area** below the curve between x=1 and x=3/

circumscribed polygon is a polygon drawn around a circle **Area** **of** Triangle The **area** **of** a triangle can be calculated by b = base h = height A = **area** h b Quadrilaterals A quadrilateral is a four-sided polygon. **Examples** include the square, rhombus, trapezoid, and **trapezium**: Parallelograms A parallelogram is a four-sided polygon with both pairs **of** opposite sides parallel. **Examples** include the square, rectangle, rhombus, and rhomboid. A/

, you will learn how to find the **areas** **of** rectilinear figures given their vertices. 7.2 **Areas** **of** Triangles and Quadrilaterals Objectives In this lesson you will learn how to find the **areas** **of** rectilinear figures given their vertices. Coordinate Geometry **Area** **of** Triangles ABC is a triangle. We will find its **area**. Construct points D and E so that ADEC is a **trapezium**. **Example** Construct points D, E and F/

you try...find the surface **area**! **Example**: C B SideAreaNo **of** Sides **Area** 2m 11m 2m To find the surface **area** **of** a shape, we calculate the total **area** **of** all **of** the faces. A cuboid has 6 faces. The top and the bottom **of** the cuboid have the same **area**. Surface **area** **of** a cuboid To find the surface **area** **of** a shape, we calculate the total **area** **of** all **of** the faces. A cuboid has 6/

the **area** **of** a rectangle work out the **area** **of** a parallelogram calculate the **area** **of** shapes made from triangles and rectangles calculate the **area** **of** shapes made from compound shapes made from two or more rectangles, for **example** an L shape or T shape calculate the **area** **of** shapes drawn on a grid calculate the **area** **of** simple shapes work out the surface **area** **of** nets made up **of** rectangles and triangles calculate the **area** **of** a **trapezium**/

the **area** **of** a rectangle work out the **area** **of** a parallelogram calculate the **area** **of** shapes made from triangles and rectangles calculate the **area** **of** shapes made from compound shapes made from two or more rectangles, for **example** an L shape or T shape calculate the **area** **of** shapes drawn on a grid calculate the **area** **of** simple shapes work out the surface **area** **of** nets made up **of** rectangles and triangles calculate the **area** **of** a **trapezium**/

terms inscribed and circumscribed are associated with the creation **of** triangles and other polygons, as well as **area** calculations. Triangles **Area** **of** a Triangle The **area** **of** a triangle can be calculated by.5(bh). b = base h = height A = **area** A =.5(bh) Quadrilaterals A quadrilateral is a four-sided polygon. **Examples** include the square, rhombus, trapezoid, and **trapezium**: Parallelograms A parallelogram is a four-sided polygon with/

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