Area of a Circle

How in the world would you find the area of a circle?

Remember!Area is always measured in square units.

Let’s look at a rectangle. Area = (Length)(Width)

(Hint: you’re counting the number of squares inside of the

rectangle)

2

4

A = L x WA = (4)(2)

A = 81 2 3 4

5 6 7 8 There are 8 squares in the

rectangle.

Now consider a circle.Estimate the number of square units

inside the circle.

There are about 13 square units inside this circle.

There are about 12 squares plus the 4 parts that are approximately of a square each.

141 2

345

6 7

8

910

11 12

This is just an ESTIMATE though. How can we find the exact area?

Area of a Circle

So the area of the circle is:

Area =πr2

But where does this formula come from?

Let’s watch a video to find out. http://www.youtube.com/watch?v=YokKp3pwVFc

Park employees are fitting a top over a circular drain in the park. If the radius of the drain is 14 inches, what is the

area of the top that will cover the drain?

Area = πr2

Area = π(14)2

Area = (3.14)(14)2

Area =(3.14)(196)Area = 615.44 in²Remember: We use 3.14 for π. Always round to the nearest

hundredth.

A circular flower bed in Kay’s backyard has a diameter of 9 feet. What is the area of the flower bed?

Area = πr2

Area = π(4.5)2Area =(3.14)

(4.5)2Area = (3.14)(20.25)Area = 63.59

ft²NOTICE: We have the diameter but we need to find the radius.

Remember: We use 3.14 for π. Always round to the nearest hundredth.

The central performance area at a circus is a circular ring having a diameter of 42 ft. Half of the ring will be used for the clown show and half will be used for the unicycle show. How much area does each group get to perform in?

2rA

44114.3 A

221A

274.1384 ftA

A = 1384.74 ÷ 2 = 692.37

Find the radius: 42/2 = 21 ft

2ft

Find the area of the square and subtract the area of the circle.

How would you find the shaded area?

ASQUARE = (2)(2)ASQUARE = 4 ft²ACIRCLE = π(1)²ACIRCLE = 3.14 ft²ASHADED = 4 - 3.14ASHADED = 0.86 ft²

Practice:Area Worksheet