In this section we will discuss area of trapezoid.
Trapezoid is a quadrilateral whose two sides are parallel to each other. In trapezium (trapezoid) ABCD such that AB and CD area parallel sides where AD and BC are its non-parallel sides.
Here, the length of parallel sides are a and b and the distance between them is h.
•Area of trapezium = 1/2 ( sum of two bases ) x height •Area = 1/2 x (a + b) x h. • Median of trapezoid = ( a + b) / 2
Base : Each of the two parallel sides of a trapezoid is called a base of trapezoid.
Altitude or height : The distance between the two parallel sides is called the height or altitude of the trapezoid.
Median of trapezoid :Its length equals the arithmetic mean of the lengths of the bases.
Some solved examples
1) Find the area of trapezoid whose parallel sides are of lengths 10 cm and 12 cm and the distance between them is 4 cm. Solution :
Two parallel sides, a = 10 cm and b = 12 cm; height =h = 4 cm.
Area = ½ x ( a + b) x h
Area = ½ x ( 10 + 12 ) x 4
Area = ½ x 22 x 4
Area = 44 cm2
2) Find the sum of the lengths of the bases of a trapezoid whose height is 11 cm and area is 0.55 m2. Solution :
Height = h = 11 cm = 11 / 100 = 0.11 m; Area = 0.55 m2
Area = ½ x (a +b) x h
0.55 = ½ x (a + b) x 0.11
(a + b) =( 0.55 x 2) / 0.11
( a + b) = 10 cm
∴ Sum of parallel sides = 10 cm.
3) Find the area of the following figure. Solution :
Area of trapezium = ½ x (a + b) x h
= ½ x ( 18 + 7) x 8
Area of trapezium = 100 cm2
Area of square = side x side
= 18 x 18
Area of square = 324 cm2
∴ Area of (ABCDEF ) = Area of trapezium + Area of square
⇒ = 100 + 324
Area of (ABCDEF ) = 424 cm2
4) Find the median of the following trapezoid. Solution :
Median of trapezoid = ( a + b) / 2
= ( 6 + 8) / 2
∴ Median of trapezoid = 7 cm.