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

The given figure is:

Given:
AD = 10 cm, AG = 8 cm, AH = 6 cm, AF = 5 cm
BF = 5 cm, CG = 7 cm, EH = 3 cm
∴ FG = AG - AF = 8 - 5 = 3 cm
And, GD = AD - AG = 10 - 8 = 2 cm
From given figure:
Area of Pantagon = (Area of triangle AFB) + (Area of trapezium FBCG) + (Area of triangle CGD) + (Area of triangle ADE)
\[= (\frac{1}{2}\times AF \times BF) + [\frac{1}{2} \times (BF + CG) \times (FG)] + (\frac{1}{2} \times GD \times CG) + (\frac{1}{2}\times AD \times EH)\]
\[=(\frac{1}{2} \times 5 \times 5) + [\frac{1}{2} \times (5 + 7) \times (3)] + (\frac{1}{2} \times 2 \times 7) + (\frac{1}{2}\times 10 \times 3)\]
\[= (\frac{25}{2}) + [\frac{36}{2}] + (\frac{14}{2}) + (\frac{30}{2})\]
\[ = 12 . 5 + 18 + 7 + 15\]
\[ {=52.5 cm}^2\]