In the figure, ABCD is a square. Area of the shaded portion is:

The correct answer is Option (1) → 90 sq. units

The shaded part is the whole square minus the two white right triangles, DGF at corner D and EBC at corner B. Their legs come from the lengths marked on the figure, since every side of the square is 12.

Triangle DGF (right angle at D):

• DG, the side AD less AG \(=12-4=8\)

• DF, the side DC less FC \(=12-6=6\)

• Area, half the product of the legs \(\displaystyle =\frac{1}{2}\times8\times6=24\)

Triangle EBC (right angle at B):

• Legs marked on the figure: EB \(=5\) and BC \(=12\)

• Area, half the product of the legs \(\displaystyle =\frac{1}{2}\times5\times12=30\)

Shaded area:

• Area of the whole square \(=12\times12=144\)

• Shaded area \(=144-24-30=90\) sq. units