Question

In square ABCD, Find the area of shaded region.

Answer 1

In square ABCD,
AB = BC = CD = AD = 20 cm
Area of square ABCD = $(side{)}^2={20}^2=400c{m}^2$
In $△$CFB, B is a right angle.
Area of $△$CFB = $\frac{1}{2}\times base\times height=\frac{1}{2}\times BF\times BC=\frac{1}{2}\times 10\times 20=100c{m}^2$
In $△$CDE, D is a right angle.
Area of $△$CDE = $\frac{1}{2}\times base\times height=\frac{1}{2}\times DE\times CD=\frac{1}{2}\times 8\times 20=80c{m}^2$
In $△$EAF, A is a right angle.
Area of $△$EAF$=\frac{1}{2}\times base\times height=\frac{1}{2}\times AF\times EA=\frac{1}{2}\times 10\times 12={60}^c{m}^2$
Area of shaded region = Area of square ABCD - (Area of $△$CFB + Area of $△$CDE + Area of $△$EAF)
= 400-(100+80+60)
= 400 - 240
= 160 $c{m}^2$
Therefor, area of shaded region is 160 sq.cm.