Q.10 In the following figures, find the area of the shaded portion.

(i) Area of the rectangle = l × b
= 18 cm × (6 cm + 4 cm) = 18 cm × 10 cm =\( 180 cm^2\) Area of right triangle \(\triangle \)AEF
=\(\frac{1}{2} ×b×h= \frac{1}{2} ×6×10=30 cm^2 \)
Area of right \(\triangle BCE = \frac{1}{2} × b × h = \frac{1}{2} × 8 × 10 =40 cm^2 \)
Area of the two right triangles =\( 30 cm^2 + 40 cm^2 = 70 cm^2 \)
Area of the shaded portion
= \( 180 cm^2 – 70 cm^2 = 110 cm^2 \)
(ii) Area of the square PQRS =\( (Side)^2 = (20)^2 = 400 cm^2 \)
Area of right triangle \(\triangle \)TSU
=\(\frac{1}{2} ×b×h= \frac{1}{2} ×10×10=50 cm^2 \)
Area of right triangle \(\triangle \)QRU
=\(\frac{1}{2} ×b×h= \frac{1}{2} ×20×10=100 cm^2 \)
Area of right triangle \(\triangle \)PQT
=\(\frac{1}{2} ×b×h= \frac{1}{2} ×20×10=100 cm^2 \)
Area of the three triangles
\( = 50 cm^2 + 100 cm^2 + 100 cm^2 = 250 cm^2 \)
Area of the shaded portion
=\( 400 cm^2 – 250 cm^2 = 150 cm^2 \)