Area of Plane Shapes

The distance around a circle is called its circumference. The distance across a circle through its center is called its diameter. We use the Greek letter (pronounced PI) to represent the ratio of the circumference of a circle to the diameter. In the last lesson, we learned that the formula for circumference of a circle is: . For simplicity, we use = 3.14. We know from the last lesson that the diameter of a circle is twice as long as the Radius. This relationship is expressed in the following formula: .

	The area of a circle is the number of square units inside that circle. If each square in the circle to the left has an area of 1 cm2, you could count the total number of squares to get the area of this circle. Thus, if there were a total of 28.26 squares, the area of this circle would be 28.26 cm2 However, it is easier to use one of the following formulas:
	or
where is the area, and is the radius. Let's look at some examples involving the area of a circle. In each of the three examples below, we will use = 3.14 in our calculations.

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Example 1:	The radius of a circle is 3 inches. What is the area?
Solution:
	= 3.14 · (3 in) · (3 in)
	= 3.14 · (9 in2)
	= 28.26 in2
Example 2:	The diameter of a circle is 8 centimeters. What is the area?
Solution:
	8 cm = 2 ·
	8 cm ÷ 2 =
	= 4 cm
	= 3.14 · (4 cm) · (4 cm)
	= 50.24 cm2
Example 3:	The area of a circle is 78.5 square meters. What is the radius?
Solution:
	78.5 m2 = 3.14 · ·
	78.5 m2 ÷ 3.14 = ·
	25 m2 = ·
	= 5 m

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Summary	Given the radius or diameter of a circle, we can find its area. We can also find the radius (and diameter) of a circle given its area. The formulas for the diameter and area of a circle are listed below:
	or