Question

if the perimeter of a trapezium 52 cm, its non parallel sides are equal to 10 cm each and its altitude is 8 cm, find the area of the trapezium

Answer 1

From Pythagoras\' theorem

10² = 8² - x²

x² = 36

x = 6

so, base of the right-angled triangles is 6cm.

The shorter parallel side of the trapezium = x,

The longer parallel side will = x + 2*6 = x + 12

P = x + x + 12 + 10 + 10 = 52

2x = 20

x = 10

Finally the side lengths of the trapezium are 10, 10, 10 and 22.

A = h/2(a + b)

= 8/2 x 32

= 4 x 32

= 128cm²