Question

A trapezium has an area of 570 cm². The height of the trapezium is 5 cm and the larger parallel side is twice in length as the smaller parallel side. find the length of the larger side.
[2 marks]

Answer 1

Let h be the height of a trapezium, 'a' be the length of a larger parallel side and 'b' be the length of a smaller parallel side.

Area of trapezium is given by:

$\text{A}=\frac{1}{2}\times (a+b)\times h$

Since larger parallel side is twice in length as the smaller parallel side
$\Rightarrow a=2b$ (1 marks)
$\Rightarrow \text{A}=\frac{1}{2}\times (2b+b)\times h$

$\Rightarrow \text{A}=\frac{3b\times h}{2}$

$\Rightarrow 570=\frac{3b\times 5}{2}$ $\Rightarrow b=76cm$$\Rightarrow a=2b=2\times 76=152cm$ (1 marks)