The given figure shows a rectangle ABCD and a right triangle BOC. Find the area of the shaded portion.

Given:

Length of rectangle = 20 cm

Breadth of rectangle = 10 cm

Height of triangle = 8 cm

Hypotenuse of triangle = 10 cm

Applying pythagoras theorem in triangle COB, we get:

BC² = OB² + OC²

⇒ (10)² = OB² + (8)²

⇒ 100 = OB² + 64

⇒ OB² = 100 - 64

⇒ OB² = 36

⇒ OB = $\sqrt{36}$

⇒ OB = 6 cm

Area of shaded figure = area of rectangle - area of triangle

As we know that area of rectangle = length x breadth

And, area of the triangle = $\dfrac{1}{2}$ x base x height

So, Area

$= 20 \times 10 - \dfrac{1}{2} \times 6 \times 8\\[1em] = 200 - \dfrac{1}{2} \times 48\\[1em] = 200 - 24\\[1em] = 176 \text{ cm}^2$

Hence, the area of the shaded portion is 176 cm².