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Area of the parallelogram

Area of the parallelogram. The line joining the two opposite vertices of the parallelogram is called a diagonal and it splits the parallelogram into two identical triangles. So the area of the parallelogram is 2 X height X base Area of the parallelogram = base X height.

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Area of the parallelogram

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  1. Area of the parallelogram The line joining the two opposite vertices of the parallelogram is called a diagonal and it splits the parallelogram into two identical triangles. So the area of the parallelogram is 2 X height X base Area of the parallelogram = base X height

  2. If the area is given and the base or the height is needed area base X height Base = area height Height = area base Example 1 : ABCD is a parallelogram whose base is 12 c.m. and height Area of the parallelogram = base X height = 12 X 15 = 180

  3. Example 2 : • A parallelogram with area 84 and base 12 cm find its height • Height = Area base • = 84 12 = 7 cm. • Evaluation • Find the area of the parallelogram if the base = 20 cm and its height = 14 cm.

  4. Area of the square in terms of its diagonals • The area of the square = side X side • The square has two equal diagonals and perpendicular • to each other . • Area of the square = X diagonal X diagonal • Example : • Find the area of a square whose diagonal length 8 cm. • Area of the square = X diagonal X diagonal = X 8 X 8 = 32

  5. Example 2: • A square shaped piece of land with diagonal length 28 m. • a square shaped house with side length 15 m. has been built on it and the left part was used as a garden , find the area of the garden. • Area of the whole land = X diagonal X diagonal • = X 28 X 28 = 392 • Area of the house = side X side • = 15 X 15 = 225 • Area of the garden = 392 – 225 = 167 • Evaluation:find the area of a square whose diagonal 18 cm.

  6. Area of the rhombus • The diagonals of the rhombus are not equal but they bisect each other • The area of the rhombus = X diagonal 1 X diagonal 2 • The area of the rhombus = base X height • Example : • Find the area of a rhombus whose diagonals are 5 and 6 cm. • Area of the rhombus = X diagonal 1 X diagonal 2 • = X 5 X 6 = 15 • Evaluation : Find the area of a rhombus whose diagonals are 14cm. and 16 cm.

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