Question

If the perimeter of a trapezium be 52cm, it's non parallel sides are equal to 10cm each and it's altitudes is 8cm, find the area of the trapezium.

Answer 1

Using Pythagoras' theorem, substitute in the values of the non-parallel side and the altitude: 
10² = 8² - x² 
x² = 36 
x = 6 

Therefore the base of the right-angled triangles is 6cm. 

If we let the shorter parallel side of the trapezium = x, the longer parallel side will = x + 12. 

P = x + x + 12 + 10 + 10 = 52 
2x = 20 
x = 10 

Therefore 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

Answer 2

Total perimeter= 52 cm
Sum of non-parallel sides= 10+10=20 cm
Therefore sum of parallel sides= 52-20=32

Area of a trapezium= 1/2×(Sum of parallel sides)×Height
                               =1/2×32×8
                               =16×8
                               =128cm²