How to Find the Area of a Circle With Cut Outs
A simple geometric formula will help you find the area of a circle, according to the Centre for Innovation in Mathematics Teaching, an educational research center in England. But for more complicated problems---such as finding the area of a circle with cutouts---some additional steps are necessary beyond the use of a simple calculation. Although the solution may seem daunting, it is a straightforward process, once you divide the problem into concrete steps.
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Instructions
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Determine the radius of the circle. Measure the distance between the center point of the circle and the edge of the circle; you may also measure the diameter of the circle and divide that by two, since the radius is half of the diameter.
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Calculate the total area of the circle, without cutouts. Square the radius---that is, multiply the radius times itself---and then multiply the result by 3.1415, or pi. For example, a circle with a radius of 8 cm would have a total area of 201.056 (8 x 8 x 3.1415).
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Measure the cutouts. If they are circular cutouts, determine the radius of each circle. If they are squares or rectangles, measure the length and width of each cutout. For a triangular cutout, measure the length of one side and the distance between that side and the point opposite that side.
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Calculate the area of the cutouts. For circular cutouts, square the radius and then multiply by 3.1415. For example, a circular cutout with a radius of 2 cm would have an area of 12.566. For square or rectangular cutouts, multiply length times width---so if you had a rectangular cut out that was 2 cm long and 4 cm wide, your cutout would have an area of 8 cm. Calculate the area of triangular cutouts by multiplying the length of one side times 1/2; take the result of this calculation and multiply it by the measurement between that side and the point opposite---also called the "height" of the triangle. For example, a triangular cutout with a base length of 2 cm and a height of 4 cm, the cut out's area would be 4 cm (1/2 x 2 x 4).
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Figure area of the circle, with the cutouts. Subtract the total area of the cutouts from the total area of the circle. The result is the area of the circle. For example, a large circle with a radius of 8 cm that had a circular cutout with a radius of 2 cm would have a total area of 188.49 (201.056 -- 12.566).
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