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Lesson 84: Area of a Circle
In this quick and easy lesson, we'll learn how to determine the area of a circle.
First, review Lesson 58 where you learned about the parts of a circle, and Lesson 83 where we introduced the concept of π. Also review the previous lessons on area in general. Just like when we had to find the circumference of a circle, we'll need a special formula to find the area of a circle, since circles don't have straight lines.
The area of a circle is defined as: A = πr2. Memorize this formula. Let's find the area of a circle whose radius is 6 cm. We have A = (3.14)(6)2. According to PEMDAS, we must first do our squaring before we multiply. We now have (3.14)(36), which is 113.04. Let's round our answer to 113. We can't leave our answer like that, though.
Whenever we work with area, our answer must always be in units squared. Our answer is 113 cm2. It may seem odd, but what this means is that inside our circle, we can fit 113 unit squares, each measuring 1cm x 1cm. The squares along the edges would have to be cut, since our border is circular, but if we arranged all the cut off pieces neatly, we would end up with 113 squares.
Let's try another one. What is the area of a circle with a diameter of 13 cm? Don't be tricked. Our formula involves the radius. We know that the radius is half the diameter, which is 6.5 cm. We'll do (3.14)(6.5)2. First we'll do our squaring, so we now have (3.14)(42.25), which is 132.665. Let's round it to 133, and we must write 133 cm2.
Later you'll have much more practice with this formula. Be sure to memorize it.
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