Question

Length of the rectangle is 8cm and breadth is 6cm in a circle. Find the area of the shaded portion.​

Answer 1

Given:

• Length of rectangle = 8cm
• Breadth of rectangle = 6cm

To Find:

• Area of shaded portion?

Solution:

In rectangle ABCD,

• Length (AB) = 8cm
• Breadth(BC) = 6cm

Therefore,

Area of rectangle = Length × Breadth

→ Area of rectangle = 8 × 6

→ Area of rectangle = 48cm² •••••(i)

In ∆ADC,

• Height (AD) = 6cm
• Base (DC) = 8cm
• Hypotenuse (AC) = ?

By usin Pythagoras theorem,

(Height)² + (Base)² = (Hypotenuse)²

→ (AD)² + (DC)² = (AC)²

→ 6² + 8² = (AC)²

→ 36 + 64 = (AC)²

→ 100 =(AC)²

→ AC = √100

→ AC = 10cm

Since AC is the diameter of circle,

Thus,

Diameter of circle = 10cm

→ Radius of circle = 5cm

Now,

Area of circle = πr²

→ Area of circle = (22/7) × 5²

→ Area of circle = (22/7) × 25

→ Area of circle = 78.6 (Approx)

→ Area of circle = 78.6cm² •••••(ii)

__________________________

We found that Area of circle is 78.6cm² and Area of rectangle under circle is 48cm².

So,

Area of shaded portion will be Area of circle - Area of rectangle.

→$\small{\bf{Area_{(shaded~portion)}~=~Area_{(circle)}~-~Area_{(rectangle)}}}$

→$\small{\bf{Area_{(shaded~portion)}}}$ = 78.6 - 48

→$\small{\bf{Area_{(shaded~portion)}}}$ = 30.6

Therefore,

Area of shaded portion = 30.6cm²