Question

find the area of shaded region​

Answer 1

Answer:

draw a line parallel to AD through E

AD=EB=12cm

area of rectangle AEDB=12*6=72cm²

area of trepizium BCFE=1/2h(a+b)

1/2(6)(12+8)

=3*20=60 cm²

area of shaded region =72+60=132cm²

Answer 2

Solution!!

Construction:-

→ Extend AE and CF till they meet.

Now, the whole figure is a square with the side 12 cm. We have to find out the area of the square.

Given:-

→ AE = 6 cm

→ FC = 8 cm

→ AB = BC = CD = DA = 12 cm

→ Side = 12 cm

→ Area = (Side)²

→ Area = (12 cm)²

→ Area = 144 cm²

Now, we have to find out the area of the ∆EBF.

→ EB = AB - AE

→ EB = 12 cm - 6 cm

→ EB = 6 cm

→ BF = BC - FC

→ BF = 12 cm - 8 cm

→ BF = 4 cm

→ Base (EB) = 6 cm

→ Height (BF) = 4 cm

→ Area = $\sf \dfrac{1}{2}\times Base\times Height$

→ Area = $\sf \dfrac{1}{2}\times 6\:cm\times 4\:cm$

→ Area = 12 cm²

Now, we will subtract the area of triangle from the area of the square. The subtracted area will be the area of the shaded portion.

→ Area of shaded region = Area of square - Area of triangle

→ Area of shaded region = 144 cm² - 12 cm²

→ $\blue{\sf Area\:of\:shaded\:region=132\:cm^{2}}$