Question

A trapezium has an area of 570 cm². The height of the trapezium is 5 cm and the longer parallel side is twice the length of the shorter parallel side. Select the statements that hold true.

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

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 'h' be the height of a trapezium, 'a' be the length of a longer parallel side and 'b' be the length of a shorter parallel side.

Area of trapezium is given by:

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

Since longer parallel side is twice in length as the smaller parallel side
$\Rightarrow a=2b$

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

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

$\Rightarrow 570=\frac{3b\times 5}{2}$ [height of the trapezium is 5 cm]

$\Rightarrow \frac{570\times 2}{5}$ = 3 b

$\Rightarrow b=76cm$

$\Rightarrow a=2b=2\times 76=152cm$