How to Find the Area of a Semicircle

In geometry, the study of the circle is an important topic. From early-recorded history, man used various methods to measure the area of a circle. Today, students taking geometry must learn to calculate the areas of circles and semi-circles. Knowing the formula that relates pi (or π, which is approximately 3.14) and radius can help you to calculate the area of a circle. Once you have the area of a full circle, finding the area of a semi-circle is relatively simple.

Things You'll Need

• Compass
• Ruler

Instructions

1. Know that to find the area of a semicircle, you use the formula for the area of a circle which is given as:
   A = π x (r ^2 )
   Then divide this by 2.

2. Practice finding the area of a semicircle with this problem. Calculate the area of a semicircle that has a diameter of 10 inches.

3. Calculate the radius of this circle. Since the diameter is 10 inches then the radius is 10/2 = 5 inches.

4. Calculate the area of the circle by plugging the radius value 5 into the formula from Step 1, for a value of:
   A= π(5x5) = 25 π sq. in.
   You can express the area in this way or use the approximation for pi as 3.14. Multiplying 3.14 x 25, you find that the area of the circle is 78.5 sq. in.

5. Divide the area of the circle by 2 to get the area of the semicircle:
   (78.5)/2 = 39.25 sq. in.
   Note that if you express the area of this circle as 25 π then you need to divide this by 2 to get 12.5 π sq. in. for the area of the semicircle.

References

• Cool Math
• Math Goodies
• University of Regina-MathCentral

Resources

• Find Information on Circles and Area