Question

If the lengths of the parallel sides of an isosceles trapezium are $20cm$ and $30cm$ and the area is $10c{m}^2$, then what is the length of the non-parallel sides ?

• A. $\sqrt{41}cm$
• B. $\sqrt{42}cm$
• C. $\sqrt{40}cm$
• D. $\sqrt{39}cm$

Answer 1

The correct option is A $\sqrt{41}cm$

Area of the trapezium $=\frac{1}{2}(AB+EF)\times$ height
$\Rightarrow 100=\frac{1}{2}\times (20+30)\times h$

$\Rightarrow h=4$

$\Rightarrow AC=BD=4cm$
$\therefore EA=BF=\sqrt{A{C}^2+E{C}^2}=\sqrt{16+25}=\sqrt{41}cm$