Question

Find the area of the pentagon shown in fig. 20.48, if AD = 10 cm, AG = 8 cm, AH = 6 cm, AF = 5 cm, BF = 5 cm, CG = 7 cm and EH = 3 cm.

Answer 1

$\text{The given figure is:}$


$$\begin{gathered} \text{Given:} \\ \text{AD = 10 cm, AG = 8 cm, AH = 6 cm, AF = 5 cm} \\ \text{BF = 5 cm, CG = 7 cm, EH = 3 cm} \\ \therefore \text{FG = AG - AF = 8 - 5 = 3 cm} \\ \text{And, GD = AD - AG = 10 - 8 = 2 cm} \\ \text{From given figure:} \\ \text{Area of Pantagon = (Area of triangle AFB) + (Area of trapezium FBCG) + (Area of triangle CGD) + (Area of triangle ADE)} \\ \text{= (}\frac{1}{2}\text{× AF × BF) + [}\frac{1}{2}\times \text{(BF + CG) × (FG)] + (}\frac{1}{2}\times \text{GD × CG) + (}\frac{1}{2}\text{× AD × EH)} \\ \text{=}(\frac{1}{2}\text{× 5 × 5) + [}\frac{1}{2}\times \text{(5 + 7) × (3)] + (}\frac{1}{2}\times 2\text{× 7) + (}\frac{1}{2}\text{× 10 × 3)} \\ \text{= (}\frac{25}{2}\text{) + [}\frac{36}{2}\text{] + (}\frac{14}{2}\text{) + (}\frac{30}{2}\text{)} \\ =12.5+18+7+15 \\ {\text{=52.5 cm}}^2 \end{gathered}$$