Question

a trapezium of area 140cm has parallel sides 10cm apart and one of these sides is 16cm long. Find the length of the parallel side

Answer 1

The distance between the two parallel sides is the height of the trapezoid, so the trapezoid has a height of 10 cm. 

Then, the two parallel sides are the trapezoid's bases, so we are given that one of the bases is 16 cm. Using the fact that the area of a trapezoid with bases b₁ and b₂ and a height of h is: 
A = (1/2)(b₁ + b₂)h, 

we see that the length of the other base is: 
140 = (1/2)(16 + b₂)(10) ==> 5(b₂ + 16) = 140 
==> b₂ + 16 = 28 
==> b₂ = 12. 

Answer 2

12 cm is the answer of this question