Question

FInd the area of figure ABCDE.

• A. 25 cm²
• B. 15 cm²
• C. 16 cm²
• D. 24 cm²

Answer 1

The correct option is A 25 cm²

If we look at the figure and divide it into known figures we get,
ABDO - Square; BCD - Isosceles Triangle; AOE - Right angle Triangle

Area of ABCDE = area(ABDO) + area(△BCD) + area(△AOE)

Lets find the area of individual figures and add.
area(ABDO) = ${\text{Side}}^2=4^2=16c{m}^2$
area(△AOE) = $\frac{1}{2}\times \text{height}\times \text{base}$
= $\frac{1}{2}\times 4\times 3=6c{m}^2$
area(△BCD) = $\frac{1}{2}\times \text{height}\times \text{base}$
= $\frac{1}{2}\times 1.5\times 4=3c{m}^2$

Area of ABCDE = area(ABDO) + area(△BCD) + area(△AOE)
= 16 + 6 + 3 = 25 cm²