1. Measurement Grade 6

2. Copyright © Ed2Net Learning, Inc. 2 1. Parallelogram is a quadrilateral in which pairs of opposite sides are parallel. 2. The distance between the pairs of opposite sides of a parallelogram is called an altitude of the parallelogram. 3. The opposite sides and opposite angles of a parallelogram are equal. ABE C F D Area of Parallelograms

3. Copyright © Ed2Net Learning, Inc. 3 AB CDEG Here, AB is the base and BE is its corresponding altitude. As opposite sides of the parallelogram are equal, area of the parallelogram is closely related to the area of the rectangle. Area of the parallelogram is equal to the product of one of its bases and the corresponding altitude. i.e. A = b * h Area of Parallelograms

4. Copyright © Ed2Net Learning, Inc. 4 Area of Triangles  A triangle is a kind of polygon that has three sides.  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. ½ x b x h

5. Copyright © Ed2Net Learning, Inc. 5 Area of Trapezoids 1. Trapezoid is a quadrilateral in which one pair of opposite sides are parallel. 2. When the non parallel sides of a trapezoid are equal, the trapezoid is called an isosceles trapezoid. 3. A right trapezoid is one which has at least two right angles 4. The two parallel sides of a trapezoid are its bases, the two non parallel sides are its legs.

6. Copyright © Ed2Net Learning, Inc. 6 BA C D E F G H 5. A line segment that is perpendicular to the bases of the trapezoid is the height of the trapezoid 6. A line segment whose endpoints are the midpoints of the legs of the trapezoid is the median of the trapezoid.

7. Copyright © Ed2Net Learning, Inc. 7 But, DE = BF which is nothing but the altitude or height ‘ h’ Let, AB = b 1 and DC = b 2 be the two parallel sides of the trapezoid Therefore, Area of trapezoid, A = ½ * h (b 1 + b 2 ) BA C D E F Area of Trapezoid

8. Copyright © Ed2Net Learning, Inc. 8 Area & Circumference of Circles A circle is a set of points in a plane at a fixed distance from a fixed point. The fixed point is called the center of the circle The perimeter of the circle is called the circumference of the circle

9. Copyright © Ed2Net Learning, Inc. 9 Diameter (AOC) Chord which passes through the centre of the circle (twice the radius) Chord (DF) Straight line joining any two points on the circumference Sector (shaded area) Part of the circle bounded by two radii and an arc cut off by it Arc (DEF) Part of the circumference C A D F Segment (shaded area) Part of the circle bounded by a chord on one side and an arc on the other side. Radius (OH) Distance between the centre and any point on the circumference (half the diameter) E G H O B Quadrant (shaded area) Sector in which the two radii are perpendicular to each other Parts of a Circle

10. Copyright © Ed2Net Learning, Inc. 10 1. The ratio of circumference to diameter is a constant for a given circle which is denoted by the Greek alphabet  (Pi) 2. The perimeter of a circle is called its circumference. Circumference of a circle, C = 2  r or C =  d 3. Area of a circle, A =  (radius)² or A =  r² 4. Radius of the circle, r =  A/  5. A sector of a circle is a region enclosed by an arc of a circle and the two radii to its end points. 6. Area of a sector, A = ½ * radius * length of the arc

11. Copyright © Ed2Net Learning, Inc. 11 3D Figures 3D figures are figures which have length, width and height. In the term 3D, 3 refers to the numbers of dimensions and D refers to dimension Cylinder Rectangular Prism Cube Cone Sphere Square Pyramid

12. Copyright © Ed2Net Learning, Inc. 12  A cone has only one face, one vertex and has no edges.  A cube has six faces, 8 vertices and 12 edges.  A cylinder has 2 faces, 0 vertices and 0 edges.  A square pyramid has 5 faces, 5 vertices and 8 edges.  A rectangular Prism has 6 faces, 8 vertices and 12 edges.  A sphere has no face, no vertex and no edges. Different types of 3D figures

13. Copyright © Ed2Net Learning, Inc. 13 Face: A face is a flat surface of a 3D figure. Edge: An edge is the line segment formed where two faces meet. Vertex: A vertex is a point where two or three edges meet. Two or more are called vertices edge face vertex

14. Copyright © Ed2Net Learning, Inc. 14 Surface Area of Prism & Cylinder Surface Area of a Prism The surface area of a prism is the sum of the areas of all the sides of the prism. The formula for the surface area of a prism therefore depends on the type of prism. Surface Area of a Cylinder The surface area of a cylinder is the sum of the areas of the two bases and the lateral face of the cylinder. surface area of a cylinder = 2  r 2 + 2  rh

15. Copyright © Ed2Net Learning, Inc. 15 Types of prism The name of a prism depends upon its base polygons. If the bases are triangles, then it is a TRIANGULAR prism. A RECTANGULAR prism has bases which are rectangles. The other types of prisms are pentagonal prism, hexagonal prism and octagonal prism. Surface Area of prism: Surface Area of any prism = Lateral area + Area of two ends

16. Copyright © Ed2Net Learning, Inc. 16 Figures of prisms Triangular prism Note: A prism is named according to the shape of its base.

17. Copyright © Ed2Net Learning, Inc. 17 Edges and vertices Solid figureNumber of faces Number of edges Number of vertices Triangular prism 596 Rectangular prism 6128 Pentagonal prism 71510 Hexagonal prism 81812 Octagonal prism 102416

18. Copyright © Ed2Net Learning, Inc. 18 Volume of Rectangular Prism & Cylinder  The amount of space occupied by an object is called its volume.  The volume of a rectangular prism is given by the formula: Volume = length × width × height  The volume of a cylinder is given by the formula: Volume = π (radius) 2 x height

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21. Copyright © Ed2Net Learning, Inc. 21 Assessment 1.Find the length of the base of a parallelogram whose area is 350 in²and height 7in. 2.Find the area of a parallelogram whose base is 40 cm and the corresponding height is 7 cm. 3. Find the base of the triangle whose area is 45 in 2 and height is 10 in. 4. The area of a trapezoid is 240 cm²and its bases are 24 cm and 16 cm. Find the height of the trapezoid. 5. Find the circumference of a circle radius is 6.3 m

22. Copyright © Ed2Net Learning, Inc. 22 Assessment 6. Find the radius of the circular field whose circumference measures 3500m. 7. Name the 3D figure. 8. a) How many faces does it have? b) How many edges does it have? 9. Find the surface area of a rectangular prism with 3 cm long, 6 cm wide and 4 cm. high. 10. Find the volume of the rectangular prism whose length is 5 in, width 4 in and height 8 in.

23. Copyright © Ed2Net Learning, Inc. 23 1)The living room drawn has a bay window. An interior designer is planning to have the hardwood floors in the room refinished. What is the total area that needs to be refinished? 13 ft 16 ft 12 ft 6 ft 2ft

24. Copyright © Ed2Net Learning, Inc. 24 2) Sharon wants to buy enough potting soil to fill a window box that is 42in. Long,8 in. wide, and 6 in. high. If 1 bag of potting soil contains 576 cu. in., how many bags should she buy?

25. Copyright © Ed2Net Learning, Inc. 25 3) Design an activity to find the relationship between the volume of a cylinder and the volume of a cone with the same base and height. Describe the relationship.

26. Copyright © Ed2Net Learning, Inc. 26 You did Great Today !! Be sure to practice what we have learned.