Calculating the surface area of rectangular and circular pools is straightforward and uses math we can all remember. Kidney-shaped, or reniform, pools, on the other hand, combine the curves of a circular pool with the elongated shape of a rectangular pool. With a constantly changing width and no straight edges, you might assume the math to find the area of a kidney-shaped object is highly complex, but you'd be wrong. The calculations involve three measurements and one straightforward formula.
Measure the length of the pool along an imaginary line joining the opposite ends of the longest axis. Repeat the measurement until you are satisfied that it is correct. Record the value.
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Measure the width of the wider bulge of the kidney shape and record the value as "A." Measure the width of the smaller bulge and record that value as "B." Double-check your measurements.
Calculate the surface area, using the formula: Area = (A + B) x Length x 0.45
For example, a pool is 20 feet long and has widths of 10 and 15 feet. Substituting the dimensions into the formula gives the surface area as (10 + 15) x 20 x 0.45, or 225 square feet.
Check for errors by reversing your calculations. Divide the surface area by 0.45 times the length of the pool. If the answer is not the combined widths of the pool, there was an error in your calculations. Repeat the math until the answer is correct.