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Area of Any Triangle Area of Parallelogram Area of Kite & Rhombus Volume of Solids www.mathsrevision.com Area of Trapezium Composite Area Volume & Surface.

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Presentation on theme: "Area of Any Triangle Area of Parallelogram Area of Kite & Rhombus Volume of Solids www.mathsrevision.com Area of Trapezium Composite Area Volume & Surface."— Presentation transcript:

1 Area of Any Triangle Area of Parallelogram Area of Kite & Rhombus Volume of Solids Area of Trapezium Composite Area Volume & Surface Area Surface Area of a Cylinder Volume of a Cylinder Composite Volume Exam Type Questions

2 Sunday, 26 April Created by Mr.Lafferty Starter Questions Q1.True or false Q2.Write down the probability of picking out a number greater than 20 in the national lottery. Q3.If a = -3 and b = -4 does Q4.Calculate a 2 – 3b 2 = 57

3 Sunday, 26 April Created by Mr.Lafferty Simple Areas Definition : Area is “ how much space a shape takes up” A few types of special Areas TrapeziumRhombus and kite ParallelogramAny Type of Triangle

4 Sunday, 26 April Created by Mr.Lafferty Learning Intention Success Criteria 1.To know the formula for the area of ANY triangle. 1. To develop a formula for the area of ANY triangle. 2.Use the formula to solve problems. 2.Apply formula correctly. (showing working) (showing working) 3.Answer containing appropriate units appropriate units Any Triangle Area

5 Sunday, 26 April Created by Mr.Lafferty Any Triangle Area h b Sometimes called the altitude h = vertical height

6 Sunday, 26 April Created by Mr.Lafferty Any Triangle Area 6cm 8cm Example 1 : Find the area of the triangle.

7 Sunday, 26 April Created by Mr.Lafferty Any Triangle Area 10cm 4cm Example 2 : Find the area of the triangle. Altitude h outside triangle this time.

8 Sunday, 26 April Created by Mr.Lafferty Any Triangle Area 5cm 8cm Example 3 : Find the area of the isosceles triangle. Hint : Use Pythagoras Theorem first ! 4cm

9 Sunday, 26 April 2015 Created by Mr. Now try Ex 2.1 & 2.2 MIA Ch1 (page 6) Area & Volume 9

10 Sunday, 26 April Created by Mr.Lafferty Q3.True or false Starter Questions Q1.Find the area of the triangle. Q2.Expand out ( w - 5) (2w 2 + 2w – 5) Q4.Rearrange into the form y = y – 3x + 7 = 0 4cm 3cm 10cm

11 Sunday, 26 April Created by Mr.Lafferty Learning Intention Success Criteria 1.To know the formula for the area of a parallelogram. 1. To develop a formula for the area of a parallelogram. 2.Use the formula to solve problems. 2.Apply formula correctly. (showing working) (showing working) 3.Answer containing appropriate units appropriate units Parallelogram Area

12 Sunday, 26 April Created by Mr.Lafferty Parallelogram Area b Important NOTE h = vertical height h

13 Sunday, 26 April Created by Mr.Lafferty Parallelogram Area Example 1 : Find the area of parallelogram. 9cm 3cm

14 Sunday, 26 April 2015 Created by Mr. Now try Ex 3.1 MIA Ch1 (page 6) Area & Volume 14

15 Sunday, 26 April Created by Mr.Lafferty Starter Questions Q1.True or false 2x 2 – 72 = 2(x – 6)(x + 6) Q2.Does x 20 = Explain your answer Q3.Expand ( y - 3) (2y 2 + 3y + 2) Q4.Calculate

16 Sunday, 26 April 2015 Created by Mr.Lafferty Learning Intention Success Criteria 1.To know the formula for the area of ANY rhombus and kite. 1. To develop a single formula for the area of ANY rhombus and Kite. 2.Use the formula to solve problems. 2.Apply formulae correctly. (showing working) (showing working) 3.Answer containing appropriate units appropriate units Rhombus and Kite Area

17 Sunday, 26 April Created by Mr.Lafferty Area of a Rhombus D d This part of the rhombus is half of the small rectangle.

18 Sunday, 26 April Created by Mr.Lafferty Area of a Kite D d Exactly the same process as the rhombus

19 Sunday, 26 April Created by Mr.Lafferty Rhombus and Kite Area Example 1 : Find the area of the shapes. 5cm 2cm 9cm 4cm

20 Sunday, 26 April Created by Mr.Lafferty Rhombus and Kite Area Example 2 : Find the area of the V – shape kite. 7cm 4cm

21 Sunday, 26 April 2015 Created by Mr. Now try Ex 4.1 MIA Ch1 (page 8) Area & Volume 21

22 Sunday, 26 April Created by Mr.Lafferty Starter Questions Q1.Find the area of the parallelogram Q2.Solve the equation (ie find the root) to 1 dp x 2 + 4x – 3 = 0 Q3.A can of beans is reduce by 15% to 25p. Find the price before the reduction. Q4.The speed of light is metres per sec. True or false in scientific notation 3 x

23 Sunday, 26 April Created by Mr.Lafferty Learning Intention Success Criteria 1.To know the formula for the area of a trapezium. 1. To develop a formula for the area of a trapezium. 2.Use the formula to solve problems. 2.Apply formula correctly. (showing working) (showing working) 3.Answer containing appropriate units appropriate units Trapezium Area

24 Sunday, 26 April Created by Mr.Lafferty Trapezium Area W X Y Z 1 2 a cm b cm h cm Two triangles WXY and WYZ

25 Sunday, 26 April Created by Mr.Lafferty Trapezium Area Example 1 : Find the area of the trapezium. 6cm 4cm 5cm

26 Sunday, 26 April 2015 Created by Mr. Now try Ex 5.1 MIA Ch1 (page 9) Area & Volume 26

27 Sunday, 26 April Created by Mr.Lafferty Starter Questions Q1.Find the area of the trapezium Q2.Explain why the perimeter of the shape is 25.24cm. Q3.y varies directly as the square of x. When y = 25, x = 4 Find the value of y when x = o r = 10cm

28 Sunday, 26 April Created by Mr.Lafferty Learning Intention Success Criteria 1.To know the term composite. 1. To show how we can apply basic area formulae to solve more complicated shapes. 2.To apply basic formulae to solve composite shapes. 3.Answer containing appropriate units appropriate units Composite Areas

29 Sunday, 26 April Created by Mr.Lafferty Composite Areas We can use our knowledge of the basic areas to work out more complicated shapes. 4cm 3cm 5cm 6cm Example 1 : Find the area of the arrow.

30 Sunday, 26 April Created by Mr.Lafferty Composite Areas Example 2 : Find the area of the shaded area. 11cm 10cm 8cm 4cm

31 Sunday, 26 April 2015 Created by Mr. Now try Ex 6.1 MIA Ch1 (page 11) Area & Volume 31

32 Summary Areas Trapezium Rhombus and kite Parallelogram Any Type of Triangle

33 Sunday, 26 April 2015 Created by Mr. Now try Ex 6.2 MIA Ch1 (page 12) Area & Volume 33

34 Sunday, 26 April Created by Mr.Lafferty Starter Questions Q1.Find the area of the trapezium Q2.Calculate the perimeter of the shape. Q3.w varies inversely as the square of b. When w = 10, b = 2 Find the value of w when b = o r = 3cm

35 Learning Intention Success Criteria 1.To know the volume formula for any prism. 1.To understand the prism formula for calculating volume. 2.Work out volumes for various prisms. 3.Answer to contain appropriate units and working. appropriate units and working. Volume of Solids Prisms

36 Definition : A prism is a solid shape with uniform cross-section Cylinder (circular Prism) Pentagonal Prism Triangular Prism Hexagonal Prism Volume = Area of Cross section x length Volume of Solids

37 Definition : A prism is a solid shape with uniform cross-section Triangular Prism Volume = Area x length Q. Find the volume the triangular prism. 20cm 2 10cm = 20 x 10 = 200 cm 3 Volume of Solids

38 Definition : A prism is a solid shape with uniform cross-section Volume = Area x length Q. Find the volume the hexagonal prism. 43.2cm 2 20cm = 43.2 x 20 = 864 cm 3 Hexagonal Prism Volume of Solids

39 26-Apr-15 Created by Mr. Lafferty Maths Dept. Back Front This is a NET for the triangular prism. 5 faces 3 congruent rectangles 2 congruent triangles 10cm 4cm Net and Surface Area Triangular Prism 4cm 10cm Bottom 4cm FT BT

40 26-Apr-15 Compiled by Mr. Lafferty Maths Dept. = 2 x3 =6cm 2 Example Find the surface area of the right angle prism Working Rectangle 1 Area = l x b = 3 x10 =30cm 2 Rectangle 2 Area = l x b = 4 x 10 =40cm 2 Total Area = = 132cm 2 2 triangles the same 1 rectangle 3cm by 10cm 1 rectangle 4cm by 10cm 3cm 4cm 10cm 1 rectangle 5cm by 10cm Triangle Area = Rectangle 3 Area = l x b = 5 x 10 =50cm 2 5cm

41 26-Apr-15 Compiled by Mr. Lafferty Maths Dept. Bottom Top LS Back RS Front This is a NET for the cuboid Net and Surface Area The Cuboid 6 faces Top and bottom congruent Front and back congruent Left and right congruent 5cm 4cm 3cm 5cm 3cm 4cm 3cm 4cm

42 26-Apr-15 Compiled by Mr. Lafferty Maths Dept. Front Area = l x b = 5 x 4 =20cm 2 Example Find the surface area of the cuboid Working 5cm 4cm 3cm Top Area = l x b = 5 x 3 =15cm 2 Side Area = l x b = 3 x 4 =12cm 2 Total Area = = 94cm 2 Front and back are the same Top and bottom are the same Right and left are the same

43 Now try MIA Ex 7.1 & 7.2 Ch1 (page 14) Volume of Solids

44 Sunday, 26 April Created by Mr.Lafferty Q3.True or false Starter Questions Q1.Expand out (x – 2) ( x 2 - 3x + 4) Q2.Factorise x 2 – 2x + 1 Q4.By rearranging in y =, find the gradient and where the straight line crosses the x-axis y + 4x - 3 = 0

45 Learning Intention Success Criteria 1.To know split up a cylinder. 1.To explain how to calculate the surface area of a cylinder by using basic area. 2.Calculate the surface area of a cylinder. Surface Area of a Cylinder

46 Total Surface Area = 2πr 2 + 2πrh The surface area of a cylinder is made up of 2 basic shapes can you name them. Curved Area =2πrh Cylinder (circular Prism) h Surface Area of a Cylinder Roll out curve side  2πr Top Area =πr 2 Bottom Area =πr 2

47 Example : Find the surface area of the cylinder below: = 2π(3) 2 + 2π x 3 x 10 3cm Cylinder (circular Prism) 10cm = 18π + 60π Surface Area of a Cylinder Surface Area = 2πr 2 + 2πrh = 78π cm

48 Example : A net of a cylinder is given below. Find the diameter of the tin and the total surface area. 2r = Surface Area of a Cylinder 2πr = 25 25cm 9cm 25 π Diameter = 2r Surface Area = 2πr 2 + 2πrh = 2π(25/2π) 2 + 2π(25/2π) x 9 = 625/2π + 25 x 9 = cm

49 Now try MIA Ex 8.1 Ch1 (page 16) Surface Area of a Cylinder

50 Sunday, 26 April Created by Mr.Lafferty Q3.Calculate Starter Questions Q1.Find the area of the triangle. Q2.Factorise 9x Q4.Find the gradient and where the straight line crosses the x-axis y – 2x + 5 = 0 6cm 10cm

51 Learning Intention Success Criteria 1.To know formula. 1.To derive the formula for the volume of a cylinder and apply it to solve problems. 2.Apply formula correctly. 3.Work backwards using formula. Volume of a Cylinder

52 Volume = Area x height The volume of a cylinder can be thought as being a pile of circles laid on top of each other. = πr 2 Volume of a Cylinder Cylinder (circular Prism) x h h = πr 2 h

53 V = πr 2 h Example : Find the volume of the cylinder below. = π(5) 2 x 10 5cm Cylinder (circular Prism) 10cm = 250π cm Volume of a Cylinder

54 Other Simple Volumes Composite volume is simply volumes that are made up from basic volumes. r D r h Cylinder = πr 2 h Cylinder (circular Prism) h r

55 Now try MIA Ex 9.1 & 9.2 Ch1 (page 18) Volume of Solids

56 Sunday, 26 April Created by Mr.Lafferty Starter Questions Q1.Factorise Q2.Write down the probability of picking out a number less than 30 in the national lottery. Q3.True or false if a = -1 and b = -2 Q4.Explain why -(a 2 ) + b 2 = 5

57 Learning Intention Success Criteria 1.To know what a composite volume is. 1.To calculate volumes for composite shapes using knowledge from previous sections. 2.Work out composite volumes using previous knowledge of basic prisms. 3.Answer to contain appropriate units and working. appropriate units and working. Volume of Solids Prisms

58 Other Simple Volumes Composite volume is simply volumes that are made up from basic volumes. r D r h Cylinder = πr 2 h Cylinder (circular Prism) h r

59 Volume of a Solid Q. Find the volume the composite shape. Composite volume is simply volumes that are made up from basic volumes. Volume = Cylinder + half a sphere h = 6m r 2m

60 Volume of a Solid Q. This child’s toy is made from 2 identical cones. Calculate the total volume. Composite Volumes are simply volumes that are made up from basic volumes. Volume = 2 x cone r = 10cm h = 60cm

61 Now try MIA Ex 10.1 Ch1 (page 19) Volume of Solids

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