Question

Find the area of the given polygon if 𝐴𝐷 = 8 𝑐𝑚, 𝐴𝐻=6 𝑐𝑚, 𝐴𝐺=4 𝑐𝑚, 𝐴𝐹=3 𝑐𝑚, 𝐵𝐹=2 𝑐𝑚, 𝐶𝐻=3 𝑐𝑚 𝑎𝑛𝑑 𝐸𝐺=2.5 𝑐𝑚.

• A. $23.5c{m}^2$
• B. $43.5c{m}^2$
• C. $33.5c{m}^2$
• D. $53.2c{m}^2$

Answer 1

The correct option is A $23.5c{m}^2$

Area of Polygon ABCDE = Area of ∆AFB + Area of trapezium FBCH + Area of ∆CHD + Area of ∆ADE

Area of ∆AFB $=\frac{1}{2}\times AF\times BF=\frac{1}{2}\times 3\times 2=3c{m}^2$

Area of trapezium FBCH $=FH\times \frac{(BF+CH)}{2}=3\times \frac{(2+3)}{2}=7.5c{m}^2$

Area of ∆CHD$=\frac{1}{2}\times HD\times CH=\frac{1}{2}\times 2\times 3=3c{m}^2$

Area of ∆ADE$=\frac{1}{2}\times GE\times AD=\frac{1}{2}\times 2.5\times 8=10c{m}^2$

Area of Polygon ABCDE $=3c{m}^2+7.5c{m}^2+3c{m}^2+10c{m}^2=23.5c{m}^2$