How to Calculate Area of Four Sides
Any object that possesses four straight sides is a quadrilateral. Quadrilaterals are also polygons that are enclosed two-dimensional geometric shapes. Types of quadrilaterals include squares, rectangles, parallelograms and rhombuses, each of which have their own special formula for area calculation. If the object's shape is not known but its sides' lengths are, then the area enclosed by the four sides can be calculated by Bretschneider's Formula, which employs the measurements of the sides and diagonals, which are the two distances between opposite points of the object.
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Instructions
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1
Sum the lengths of the sides, then divide by 2. For this example, the closest side's length is 15, the length of the left side is 16, the length of the far side is 11 and the right side's length is 14. The lengths summed equal 56, and half of 56 is 28.
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2
Subtract the length of each side individually from the calculated amount of the previous step, then multiply those differences together. For this example, 15 subtracted from 28 equals 13, 16 subtracted from 28 equals 12, 11 subtracted from 28 equals 17 and 14 subtracted from 28 equals 14. These differences, 13, 12, 17 and 14, multiplied together equal 37,128.
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3
Multiply the lengths of the two diagonals together. For this example, the lengths of the diagonals are 17 and 22. Multiplying 17 by 22 results in 374.
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4
Multiply the lengths of the right and left side together and the far and nearest sides together, then sum those products. For this example, multiplying 16 by 14 equals 224 and multiplying 11 by 15 equals 165. Summing 224 and 165 results in 389.
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5
Add the product of the diagonals calculated in Step 3 to the product from the previous step. For this example, 374 added to 389 equals 763.
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6
Subtract the product of the diagonals calculated in Step 3 from the product from Step 4, then multiply that difference by the sum calculated in the previous step. For this example, 389 less 374 equals 15. Multiplying 15 by 763 results in 11,445.
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7
Divide the product from the last step by 4, then subtract it from the product calculated in Step 2. For this example, 11,445 divided by 4 equals 2,861.25 and subtracting that amount from 37,128 equals 34,266.75.
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8
Calculate the square root of the previous step's difference to find the area. For this example, the square root of 34,266.75 and the area within the four sides is 185.113.
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