Question

Find the area of the given figure, if AC = 10 cm, AD = 12 cm, and $h_1,h_2,h_3$ are 3, 4, 5 in cm respectively.

• A. 30 $c{m}^2$
• B. 48 $c{m}^2$
• C. 60 $c{m}^2$
• D. 69 $c{m}^2$

Answer 1

The correct option is D 69 $c{m}^2$

Area of triangle = $\frac{1}{2}$$\times$base$\times$height

Area of given figure
= Area of $△$ABC
+ Area of $△$ACD
+ Area of $△$AED

= $\frac{1}{2}$$\times$AC$\times$h1
+ $\frac{1}{2}$$\times$AD$\times$h2
+ $\frac{1}{2}$$\times$AD$\times$h3

= $\frac{1}{2}$$\times$10$\times$3
+ $\frac{1}{2}$$\times$12$\times$4
+ $\frac{1}{2}$$\times$12$\times$5

= $\frac{1}{2}$$\times$30 + $\frac{1}{2}$$\times$48 + $\frac{1}{2}$$\times$60
= 15+24+30 = 69 $c{m}^2$