Question

In the figure ABCD , find the area of the shaded region.

Answer 1

Here , the given figure ABCD is a square , whose each sides is 20 cm.

Area of shaded region = Area of the square - Area of the triangles i.e. ar[ EBF + EAF + CDE ]

Now ,

Area of the square = [ side ]^2

=> [ 20 ]^2

=> [ 20 ] * [ 20 ] = 400 cm^2

Hence , the area of square will be 400 cm^2

And ,

side [ DC = CB = AB = DA ] = 20 cm.

side [ AF = FB ] = 10 cm.

Then , side will be AE = AD - DE

AE = 20 - 8 = 12

Hence , the side AE = 12 cm.

Since two sides of a right triangle are perpendicular then one of the perpendicular side will be height and other will be base of a triangle.

Then , area of the will be ,

According to the question ;

=> 400 - [ 1 / 2 * 10 × 20 ] + [ 1 / 2 * 10 × 12 ] + [ 1 / 2 * 8 × 20 ]

=> 400 - [ 100 ] + [ 60 ] + [ 80 ]

=> 400 - 240

=> 160 cm^2

Hence , the area of shaded region is 160 cm^2.