Lesson 8-5 Areas of Circles

You will learn: To find the areas of circles,

The Area of a circle is the number of square units contained inside the circle. Example: Estimate the number of square units inside the circle There are about 12 squares plus the 4 parts that are approximately ¼ of a square each. There are about 13 square units inside this circle. It is hard to always count the squares so it would be a good idea to use a formula.

Most of the shapes you have you have investigated in this chapter could be divided into rectangles or triangles. Can a circle be divided into rectangles or triangles?

Make a large circle, cut it and fold the circular region in half. Fold it in half a second time, then a third time and a fourth time. Unfold your circle and cut it along the folds into 16 wedges.

Arrange the wedges in a row, alternating the tips up and down to form a shape that resembles a parallelogram. r r

Attached the two figures then seem as a parallelogram It looks very much like a parallelogram! Therefore its area = base x height Height = radius Length of the base Length of the base = ½ of the circumference

r r r A =  r 2 Area of Circle ** Units 2 Radius of circle Area of a circle

Find the area of the circle below: How to find the area of a circle given the radius If you have the radius: square it and then multiply by State the formula Substitute the values for  and r.

Find the area of the circle below: How to find the area of a circle given the diameter If you have the diameter: Divide the diameter by 2 to get the radius. State the formula Substitute the values for  and r. Square the radius and then multiply by 3.14 (  ).

Example: How much more pizza is in a 12in diameter pizza than in a 10in diameter pizza? A 12 =  r 2 =6 2  =36  =113.1in 2 A 10 =  r 2 =5 2  = 25  = 78.5in 2 36  - 25  = 11  = 34.6in 2