 You can estimate the area of a circle by separating the circle into small triangles and then laying out those triangles so that they form a parallelogram.

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Presentation transcript:

 You can estimate the area of a circle by separating the circle into small triangles and then laying out those triangles so that they form a parallelogram.  Once you have the parallelogram, you can approximate the area of the circle from the area formula for a parallelogram.

½ the circumference of the circle Radius of the circle

 The triangles should all be congruent.  The smaller you make the triangles the more accurate the estimation will be.

 Now you can simply find the area of the parallelogram made by the triangles using the formula for the area of a parallelogram.

½ circumference Radius

 The base of the parallelogram will not be exactly the same length as ½ the circumference of the circle.  However, as you increase the number of triangles you are using, the base of the parallelogram will get closer to ½ the circumference of the circle.

 The idea is that if you were to use an infinite number of triangles, the base of the parallelogram would be so close to ½ the circumference of the circle that we can equate them.

Area of parallelogram is equal to half the circumference of the circle times the radius of the circle. The area of the parallelogram and the circle.

 This area for the parallelogram happens to be the equation for the area of any circle.