Semicircle

Definition

A semicircle is a two-dimensional geometric shape that represents half of a complete circle. It is formed by dividing a circle along its diameter, resulting in two equal halves.

5 Must Know Facts For Your Next Test

1. The area of a semicircle is calculated as $\frac{1}{2}\pi r^2$, where $r$ is the radius of the circle.
2. The perimeter of a semicircle is calculated as $\pi r + 2r$, where $r$ is the radius of the circle.
3. Semicircles are commonly used in the design of circular objects, such as tabletops, arched doorways, and architectural features.
4. Semicircles can be used to represent the cross-section of a cylinder or the profile of a half-sphere.
5. In the context of solving geometry applications, semicircles can be used to model and calculate the area and perimeter of irregular figures that incorporate circular elements.

Review Questions

• How can the area of a semicircle be calculated, and what is the formula?
  • The area of a semicircle can be calculated using the formula $\frac{1}{2}\pi r^2$, where $r$ is the radius of the circle. This formula is derived by taking the area of a full circle, which is $\pi r^2$, and dividing it by 2 to account for the fact that a semicircle represents half of a complete circle.
• Explain how the perimeter of a semicircle is determined and what factors are involved in the calculation.
  • The perimeter of a semicircle is calculated as $\pi r + 2r$, where $r$ is the radius of the circle. This formula takes into account the curved portion of the semicircle, which is equal to $\pi r$ (half the circumference of the full circle), and the two straight line segments that form the diameter, each with a length of $r$.
• Discuss the practical applications of semicircles in the context of solving geometry problems involving circles and irregular figures.
  • Semicircles are commonly used to model and analyze the properties of circular and irregular geometric shapes in real-world applications. For example, in the context of 9.5 Solve Geometry Applications: Circles and Irregular Figures, semicircles can be used to represent the cross-section of a cylinder, the profile of a half-sphere, or the curved portions of an irregularly shaped figure. By understanding the area and perimeter formulas for semicircles, students can effectively calculate the relevant measurements and properties of these shapes, which is essential for solving practical geometry problems.

Related terms

Circle: A closed, two-dimensional shape where all points on the perimeter are equidistant from the center.

Diameter:

The length of a straight line that passes through the center of a circle, dividing it into two equal halves.

Arc:

A portion of the circumference of a circle, bounded by two points on the circle.