Question

in the adjoining figure abcd is a rectangle of size 18 cm by 10 cm. in ∆bec , angle e = 90° and ec = 8 cm. find the area of the shaded region.

Answer 1

156$cm^{2}$ is the area of the shaded region.

Step-by-step explanation:

In ΔBEC,

$BC^{2} = EB^{2} + EC^{2}$

$EB^{2} = BC^{2} - EC^{2}$

EB = $\sqrt{100 - 64}$

EB = $\sqrt{36}$ = 6cm

Area of the ΔEBC = 1/2 * EB * EC

= 1/2 * 6 * 8

= 24$cm^{2}$

Area of the rectange = l * b

= 18 * 10

= 180 sq. cm

Area of the shaded region = area of rectangle - area of ΔBEC

= 180 sq. cm - 24sq.cm

= 156 sq.cm

Learn more: find the area of the shaded region

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