Question

The area of the given trapezium is .

• A. $25c{m}^2$
• B. $30c{m}^2$
• C. $20c{m}^2$

Answer 1

The correct option is A $25c{m}^2$

Draw a line BP perpendicular to side DC.Therefore, the given image has two figures, a rectangle and a triangle.
Length of the rectangle ABPD = 4 cm
Breadth = 5 cm
$\therefore \text{Area}=length\times breadth$
$\Rightarrow \text{Area}=4\times 5=20c{m}^2$

Also,
Base of the triangle BPC = 2 cm
Height = 5 cm
$\text{Area}=\frac{1}{2}\times base\times height$
$\Rightarrow \text{Area}=\frac{1}{2}\times 2\times 5=5c{m}^2$

Therefore, area of the given trapezium
= area of rectangle ABPD + area of triangle BPC
$=20c{m}^2+5c{m}^2=25c{m}^2$