Question

The parallel sides of a trapezium are $20cm$ and $10cm$. Its non-parallel sides are both equal each being $13cm$. Find the area of the trapezium.

• A. $120c{m}^2$
• B. $180c{m}^2$
• C. $210c{m}^2$
• D. $150c{m}^2$

Answer 1

The correct option is B $180c{m}^2$

We divide the trapezium into $3$ parts: $2$ triangles and a rectangle.

Base of triangle $=\frac{20-10}{2}$$=5$

Height of the triangle and rectangle $(h{)}^2={13}^2-5^2$

$\Rightarrow (h{)}^2=144$

$\Rightarrow h=12$

Area of trapezium $=\frac{1}{2}\times$(sum of parallel sides) $\times$ (height)
$=\frac{1}{2}\times (10+20)\times \left(12\right)$

$=180sq.cm$