The area of the shaded region is the difference between two geometrical shapes which are combined together. By subtracting the area of the smaller geometrical shape from the area of the larger geometrical shape, we will get the area of the shaded region. Or subtract the area of the unshaded region from the area of the entire region that is also called an area of the shaded region.

Area of the shaded region = Area of the large geometrical shape (entire region) – area of the small geometrical shape (shaded region).

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## How to Find the Area of a Shaded Region?

Follow the below steps and know the process to find out the Area of the Shaded Region. We have given clear details along with the solved examples below.

- Firstly, find out the area of the large geometrical shape or outer region.
- Then, find the area of the small geometrical shape or inner region of the image.
- Finally, subtract an area of the small geometrical shape (entire region) from the large area of the small geometrical shape (shaded region).
- The resultant value is considered as the area of the shaded region.

### Area of the Shaded Region Examples

**Problem 1.**

A regular hexagon is inscribed in a circle with a radius of 21cm. Find out the area of the shaded region?

**Solution:**

As per the given information,

Hexagon is inscribed in a circle.

Radius of the circle = 21cm.

Area of the circle = A=πr².

Substituting the radius (r) value in the above equation, we will get

A = π(21)².

A = 22 / 7(21 * 21).

A = 22(3*21).

A = 1386.

Area of the circle (A) = 1386 cm².

Area of the hexagon = 3√3/ 2 r².

Substitute the radius value in the above equation, we will get

A = 3√3/ 2 (21)².

A = 3√3/ 2 (441).

A = 1145.75

The area of the hexagon is equal to 1145 cm².

Area of the shaded region = Area of the large geometrical shape – Area of the small geometrical shape.

Area of the shaded region = 1386 – 1145 = 241 cm².

Therefore, the area of the shaded region is equal to 241 cm².

**Problem 2.**

The square is inscribed in a rectangle. The side of the square is 2cm. The length and breadth of the rectangle is 4cm and 5cm. Find out the area of the shaded region?

**Solution:**

As per the given details,

The Square is inscribed in a rectangle.

Side of the square a = 2cm.

Length of the rectangle (l) = 4cm and breadth of the rectangle (b) =5cm.

Area of the square (A) = a²

Substitute the ‘a’ value in the above equation, we will get

Area of the square (A) = (2)² = 4cm².

Area of the rectangle (A) = l * b

Substitute the length and breadth values in the above equation, we will get

Area of the rectangle (A) = 4cm * 5cm = 20 cm².

Area of the shaded region = Area of the large geometrical shape – area of the small geometrical shape.

Area of the shaded region = 20 – 4 = 16 cm².

Therefore, the Area of the shaded region is equal to 16cm².

**Problem 3.**

A Triangle is inscribed in a Square. The side of the square is 20cm and the radius of the triangle is 7cm. Calculate the area of the shaded region?

**Solution:**

As per the given information,

A triangle is inscribed in a square.

Side of the square (a) = 20cm.

Radius of the triangle (r) = 7cm.

Area of the square (A) = a².

Substitute the ‘a’ value in the above equation, we will get

Area of the square (A) = (20)² = 400cm².

Area of the triangle (A)=πr².

Substitute the radius value in the above equation. Then we will get,

A = 22 / 7 (7)².

A = 22 * 7 =154.

The area of the triangle is equal to 154 cm².

Area of the shaded region = Area of the large geometrical shape – area of the small geometrical shape.

Area of the shaded region = 400 – 154 = 246 cm².

Therefore, the Area of the shaded region is equal to 246 cm².

**Problem 4.**

A semi-circle is inscribed in a square with a radius of 14cm. The side of the square is 25cm. Calculate the area of the shaded region?

**Solution:**

As per the given details,

A semi-circle is inscribed in a square.

Radius of the semi-circle (r) = 14cm.

Side of the square (a) = 25cm.

Area of the square (A) = a².

Substitute the ‘a’ value in the above equation, we will get

Area of the square (A) = (25)² = 625 cm².

Area of the Semi – circle (A) = πr² / 2.

Substitute the radius of the semi-circle in the above equation, we will get

A = 22 / 7 (14)² / 2.

A = 22 / 7 (14 * 14) / 2.

A = 22 (2 * 14) / 2.

A = 22 * 14 = 308.

The area of the semi-circle is equal to 308 cm².

Area of the shaded region = Area of the large geometrical shape – Area of the small geometrical shape.

Area of the shaded region = 625 – 308 = 317 cm².

So, the Area of the shaded region is equal to 317 cm².

### FAQs on finding the Area of a Shaded Region

**1. What is the Area of the Shaded Region?**

It is the difference between the area of the outer region and the inner region.

**2. How to find the Area of the Shaded Region?**

There are three steps to find the area of the shaded region. They are

i. Calculate the area of the outer region.

ii. Calculate the area of the inner region.

iii. Subtract the area of the inner region from the outer region.

**3. What is the Formula for the Area of the Shaded Region?**

The formula for the area of the shaded region is

Area of the shaded region = Area of the large geometrical shape (entire region) – area of the small geometrical shape (shaded region).