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Mensuration, , , , Area and perimeter of various shapes:, Shape, 1. Rectangle with adjacent, sides a and b, , 2. Square with side a, , Area, a×b, , Perimeter, 2(a + b), , a2, , 4a, , πr2, , 2πr, , 3. Circle with radius r, Sum of the, three sides, 4. Triangle with base b and its, corresponding height h, , b×h, , Sum of the, four sides, , 5. Parallelogram with base b and, its corresponding height h, , Area of trapezium =, between them), , , (Sum of the lengths of the parallel sides) × (Perpendicular distance, , Area of quadrilateral ABCD = Area of ∆ABC + Area of ∆ACD, = 12×d×h1 + 12×d×h2= 12×d×h1+h2

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Example: Find the area of the quadrilateral ABCD., , Solution: Area of the quadrilateral ABCD = Area of ΔABD + Area of ΔBCD, Area of triangle =12 × base × corresponding height, Area of ΔABD, Area of ΔBCD, ∴ Area of quadrilateral ABCD = 9 cm2 + 6 cm2 = 15 cm2, , , Area of rhombus, , (Product of its diagonals), , , , Area of a polygon can be calculated by breaking the polygon into triangles or any types of a, quadrilateral., Example: Find the area of the given polygon, where ABCD is a trapezium.

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Solution: Area of ABCED = Area of trapezium ABCD + Area of ∆CDE, =12×3+5×3 + 12×5×4, = 12 + 10, = 22 cm2, , , Surface areas of cuboid:, , Lateral surface area of the cuboid = 2h (l + b), Total surface area of the cuboid = 2 (lb + bh + hl), Note: Length of the diagonal of a cuboid =, Example: Find the edge of a cube whose surface area is 294 m2., Solution: Let the edge of the given cube be a., ∴ Surface area of the cube = 6a2, Given, 6a2 = 294, , , , Surface areas of cube:, , Lateral surface area of the cube = 4a2, Total surface area of the cube = 6a2, Note: Length of the diagonal of a cube =, , , Surface areas of solid cylinder, , o, , Curved surface area = 2πrh, where r and h are the radius and height

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o, , Total surface area = 2πr (r + h), where r and h are the radius and height, , Example : What is the curved surface area of a cylinder of radius 2 cm and height 14, cm?, Solution: Curved surface area of cylinder = 2πrh, , , , Surface areas of hollow cylinder, , o, , Curved surface area = 2πh (r + R), where r, R and h are the inner radius, outer radius and, height, , o, , Total surface area = CSA of outer cylinder + CSA of inner cylinder + 2 × Area of base, = 2π (r + R) (h + R – r), where r, R and h are the inner radius, outer radius and height, , , , Volume of cube and cuboid, , o, o, , Volume of cube = a3, where a is the side of the cube, Volume of cuboid = l × b × h, where l, b and h are respectively the length, breadth and height, of the cuboid., Example: What is the side of a cube of volume 512 cm3?, Solution: Volume of cube = 512 cm3

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, , Volume of the solid cylinder and hollow cylinder, , o, , Volume of solid cylinder = πr2h, where r and h are the radius and height of the solid, cylinder, , o, , Volume of the hollow cylinder = π (R2 − r2) h, where r, R and h are the inner radius, outer, radius and height of hollow cylinder, , Example: Find the volume of the pillar of radius 70 cm and height 10 m., Solution: Radius of the pillar (r) = 70 cm =, Height of the pillar (h) = 10 m, , = 0.7 m