Question

A trapezium has an area of $570c{m}^2.$ The height of the trapezium is $5cm$ and the larger parallel side is twice the smaller parallel side. Choose the correct option.

• A. Length of the larger side is 152 cm
• B. Length of the smaller side is 76cm
• C. Length of the smaller parallel side is $38cm$
• D. Length of the larger parallel side is $76cm$

Answer 1

Answer: (A), (B)

The correct options are
A

Length of the larger side is 152 cm

B

Length of the smaller side is 76cm

Let ${}^{\prime }{h}^{\prime }$ be the height of a trapezium, ${}^{\prime }{a}^{\prime }$ be the length of the smaller parallel side and then ${}^{\prime }2a^{\prime }$ will be the length of the larger parallel side.

Area of trapezium is given by = $\frac{1}{2}\times$ sum of parallel sides $\times$ distance between parallel sides

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

$=\frac{1}{2}\times 3a\times h$

$\Rightarrow 570=\frac{15a}{2}$ [$\because h=5cm$]

$\Rightarrow a=\frac{570\times 2}{15}=76cm$

$\Rightarrow \text{Length of larger parallel side,}2a=2\times 76=152cm$