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# Understanding Semicircles in Geometry

## What Is a Semicircle?

A semicircle is a geometric shape with one curved side and two straight sides. It is a half of a circle, hence the name. A semicircle is formed by taking a circular arc and connecting its endpoints to form a straight line. The curved side of a semicircle is called a semicircular arc, and the straight sides are called the diameter of the semicircle.

## How Is the Radius of a Semicircle Measured?

The radius of a semicircle is the distance from the center of the semicircle to any point on the semicircular arc. The diameter of a semicircle is the length of the straight line that connects the two endpoints of the semicircular arc. The radius of a semicircle is always equal to half of its diameter.

## How Is the Area of a Semicircle Calculated?

The area of a semicircle can be calculated using the following formula:

This formula is derived from the area of a circle formula, which is p x (Radius)2. Since a semicircle is half of a circle, the area formula for a semicircle is half of the area formula for a circle.

## What Are Some Applications of Semicircles in Geometry?

Semicircles are commonly used in a variety of geometric problems. For example, semicircles can be used to calculate the area of a sector of a circle, or the area of an isosceles triangle. They can also be used to calculate the circumference of a circle, or the length of an arc.

## Practice Problems

1. Find the area of a semicircle with a radius of 4 cm.

Answer: Area = p x (4 cm)2 = 12.57 cm2

2. Find the circumference of a semicircle with a diameter of 12 cm.

Answer: Circumference = p x (6 cm) = 18.85 cm

3. Find the radius of a semicircle with an area of 25 cm2.

4. Find the diameter of a semicircle with a circumference of 24 cm.

Answer: Diameter = (24 cm) / p = 7.65 cm

5. Find the area of a sector of a circle with a radius of 8 cm and an arc length of 24 cm.

Answer: Area = (24 cm x (8 cm)2) / (2 x p) = 38.48 cm2

## Summary

In this article, we have discussed semicircles in geometry. We learned that a semicircle is a geometric shape with one curved side and two straight sides, and that the radius of a semicircle is always equal to half of its diameter. We also discussed the formula for calculating the area of a semicircle and the applications of semicircles in geometry. Finally, we have provided some practice problems to help you understand and apply the concepts discussed in this lesson.

## FAQ

### What is semicircle with example?

A semicircle is a two-dimensional shape that is created by drawing a line from one end of a circle to the other. It is half of the circle and looks like half of an oval. For example, the face of a clock is a semicircle.

### What is a semicircle called?

A semicircle is also known as a hemicycle, semi-circle, or semicircle.