Circle Area: Step-by-Step Guide
The area of a circle is pi times the radius times the radius. The radius is the distance from the center to the edge. If you are given the diameter (the distance all the way across), cut it in half to get the radius. Pi is a special number that is about 3.14.
Math Racer skill guide · Middle School · Grades 6-8
How to solve it, step by step
- Find the radius. If the problem gives you the radius, use it. If it gives you the diameter, divide by 2 to get the radius.\[r = \frac{d}{2}\]
- Write the area formula. The area of a circle is pi times the radius squared.\[A = \pi r^2\]
- Put in the radius and square it. Replace r with the number. Square the radius first (multiply it by itself), then multiply by pi.\[A = \pi (r)^2\]
- Multiply by pi and write the units. You can leave pi as a symbol for an exact answer, or use 3.14 for a decimal. Area uses square units.\[A = \pi r^2 \;\text{units}^2\]
Worked example
A circle has a radius of 5 cm. Find its area, both in terms of pi and as a decimal.
Step 1: The radius is 5 cm.
Step 2: The formula is area = pi x r x r.
Step 3: Put in the number: area = pi x 5 x 5.
Step 4: Square the radius: 5 x 5 = 25. So area = 25 x pi.
Step 5: For a decimal, use pi = 3.14159: 25 x 3.14159 = about 78.54.
Step 6: Add the units: the area is 25 x pi square cm, or about 78.54 square cm.
Tips and common mistakes
- Square the radius first, then multiply by pi.
- If you are given the diameter, cut it in half first to get the radius.
- Leave your answer in terms of pi unless the problem asks for a decimal.
- Area is in square units. If the radius is in cm, the area is in square cm.
- Do not mix up the two circle formulas. Area is pi x r x r. Circumference is 2 x pi x r.
- For a half circle, find the area of the full circle and then cut it in half.
- Squaring is not doubling. 5 squared is 25, not 10.
- Draw a quick picture if you are not sure whether you were given the radius or the diameter.