Question

In the given fig. ABC is a quadrant of a circle of radius 10cm and a semi-circle is drawn with BC as diameter. Find the area of shaded region.

Answer 1

Answer:

10.71 sq. cm

Step-by-step explanation:

pls see the attached solution

Answer 2

Given :

• ABC is a quadrant of a circle of radius 10cm.
• A semi-circle is drawn with BC as diameter.

To Find :

• The area of shaded portion.A

Solution :

_______________________

Case : I

• Finding the area of quadrant of the circle which is of radius 10

Using Formula : Area of sector = θ/360 πr²

We have,

• θ = 90° [As the angle is a quadrant of circle]
• r = 10 cm.

Putting the values

༒ Area of sector = θ/360 πr²

$\longrightarrow$ 90/360 × 3.14 × 10²

$\longrightarrow$ 1/4 × 3.14 × 100

$\longrightarrow$ 1/4 × 314

$\longrightarrow$ 78.5 cm²

_______________________

Case : II

• Finding area of triangle ∆ABC

Using Formula : Area of triangle = 1/2 × base × height

We have,

• Base = 10 cm.
• Height = 10 cm.

Putting the values

༒ Area of triangle = 1/2 × base × height

$\longrightarrow$ 1/2 × 10 × 10

$\longrightarrow$ 1/2 × 100

$\longrightarrow$ 50 cm²

_______________________

Case : III

• Finding length of BC

Using Pythagoras theorem : BC² = AB² + AC²

We have,

• AB = 10 cm.
• AC = 10 cm.

Putting the values

༒ BC² = AB² + AC²

$\longrightarrow$ BC² = 10² + 10²

$\longrightarrow$ BC² = 100 + 100

$\longrightarrow$ BC² = 200

$\longrightarrow$ BC = √200

$\longrightarrow$ BC = 14.14 cm

_______________________

Case : IV

• Finding the area of semi-circle is drawn with BC as diameter

Using Formula : Area of semi circle = 1/2πr²

We have,

• r = 14.14/2 = 7.07 cm.

Putting the values

༒ Area of semi circle = 1/2πr²

$\longrightarrow$ 1/2 × 3.14 × 7.07²

$\longrightarrow$ 1/2 × 3.14 × 49.98

$\longrightarrow$ 1/2 × 156.93

$\longrightarrow$ 78.46 cm²

_______________________

Case : V

• Finding area of the shaded pportion

Formula : Area of Shaded Portion = [Area of semi circle - (Area of sector - Area of triangle)]

We have,

• Area of semi circle = 78.46 cm²
• Area of sector = 78.5 cm²
• Area of triangle = 50 cm²

Putting the values

༒ Area of Shaded Portion = [Area of semi circle - (Area of sector - Area of triangle)]

$\longrightarrow$ 78.46 - (78.5 - 50)

$\longrightarrow$ 78.46 - 28.5

$\longrightarrow$ 49.96

Hence, the area of the shaded portion = 49.96 cm²