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# Area of a Semicircle

## Semicircle Area Formula

The formula for area of a semicircle is given as:

**A = ^{1}⁄_{2}πr^{2}**

Where *A* is the area and *r* is the radius.

### Example Problems

**Problem 1:**

What is the area of a semicircle with a radius of 5?

Solution:

1.) Let’s plug the radius into the area formula.

A = ^{1}⁄_{2}πr^{2}

A = ^{1}⁄_{2}π(5^{2}) = 12.5π

2.) **The area is 12.5π.**

**Problem 2:**

A semicircle’s area is measured to be 4.5π square meters. What is the radius in meters?

Solution:

1.) Let’s plug the area into the formula.

A = ^{1}⁄_{2}πr^{2}

4.5π = ^{1}⁄_{2}πr^{2}

2.) Now we will solve for the radius *r*.

4.5 = ^{1}⁄_{2}r^{2}

r^{2} = 9

r = 3

3.) **The radius is 3 meters.**