Question

Calculate the area of the pentagon ABCDE, where AB = AE and with dimensions as shown in Fig. 36.

Answer 1

Join BE.
Area of the rectangle BCDE = CD x DE
= 10 cm x 12 cm = 120 cm²
Area of ΔABE = $\frac{1}{2}$x BE x height of the triangle
= $\frac{1}{2}$x 10 cm x (20 − 12) cm
= $\frac{1}{2}$x 10 cm x 8 cm = 40 cm²
Hence,
Area of the pentagon ABCDE = (120 + 40) cm² = 160 cm²