• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
Geometry Help
  • About
  • Privacy Policy
  • Contact Me
  • Terms of Service
  • Accessibility Statement
menu icon
go to homepage
search icon
Homepage link
  • About
  • Privacy Policy
  • Contact Me
  • Terms of Service
  • Accessibility Statement
×
Home » Area of Geometric Shapes » Area of Semicircle

Area of Semicircle

Last updated: Sep 30, 2019 by Ido Sarig · This website generates income via ads and uses cookies · Terms of use · Privacy policy

In today's lesson, we will discuss the formula for finding the area of a semicircle. A semicircle is half of a circle - a shape like this:

Drawing of a semicircle

It is formed by drawing the diameter of a circle - a straight line the runs from one point on the circle's circumference, through the center of the circle, and to another point on the circle's circumference on the other side.

The diameter splits the circle into two equal semicircles.

As we have discussed before, a circle is a geometric shape that is completely defined (in terms of its area or perimeter) by one property- its radius. The area of a circle is given by the formula Acircle=π*r2, where π  is a special number, which is the same for all circles, that is the ratio between a circle’s diameter and its circumference.

Since a semicircle is half of a circle- its area is simply half the area of a full circle: Asemicircle=π*r2/2.

Let's look at a simple geometry problem involving semicircles and their area.

Problem

A semicircle has a perimeter whose length is 8 units. Find its area.

Strategy

The formulas for the area and circumference of circles (and thus semicircles) are very simple. They only require knowing the length of the radius. So we will solve this using the simple formula for the area of a semicircle (Asemicircle=π*r2/2). We will get the length of the radius from the perimeter.

The perimeter of a full circle is Ccircle=2*π*r. So half a circle would be just π*r - but we also have to add the straight part forming the semicircle to get the complete perimeter. That part is simply the diameter, which is twice the radius. So Psemicircle=π*r+2r=(2+π)r. Here, Psemicircle=8, so (2+π)r=8 and r=8/(2+π).

Now that we have r, we plug it into the Area formula, and have the answer:

Asemicircle=π*r2/2 = π*[8/(2+π)]2 = π*[64/(4+4π+π2)]

« Line Parallel to the Base of a Trapezoid
Similar Trapezoids »

About the Author

Ido Sarig is a high-tech executive with a BSc degree in Computer Engineering. His goal is to help you develop a better way to approach and solve geometry problems. You can contact him at [email protected]

Primary Sidebar

About

Welcome to Geometry Help! I'm Ido Sarig, a high-tech executive with a BSc degree in Computer Engineering and an MBA degree in Management of Technology. I'm here to tell you that geometry doesn't have to be so hard! My goal with this website is to help you develop a better way to approach and solve geometry problems, even if spatial awareness is not your strongest quality. Read More…

Geometry Topics

  • Area of Geometric Shapes
  • Circles
    • Arcs, Angles, and Sectors
    • Chords
    • Inscribed Shapes
    • Tangent Lines
  • Lines and Angles
    • Intersecting Lines and Angles
    • Parallel Lines
    • Perpendicular lines
  • Pentagons and Hexagons
  • Perimeter of Geometric Shapes
  • Polygons
  • Quadrangles
    • Kites (Deltoids)
    • Parallelograms
    • Rectangles
    • Rhombus
    • Squares
    • Trapezoids
  • Triangles
    • Congruent Triangles
    • Equilateral Triangles
    • Isosceles Triangles
    • Pythagorean Theorem
    • Right Triangles
    • Similar Triangles
    • Triangle Inequalities

By accessing or using this website, you agree to abide by the Terms of Service and Privacy Policy.


Copyright © 2023