How to Find the Area of a 12 Sided Polygon
A polygon's shape depends on the number of its sides and the angles that form when those sides connect. A 12-sided polygon is known as a dodecagon. Dodecagons, like all other polygons, can be either regular or irregular. A regular dodecagon's has 12 identical sides and 12 equal connecting angles, whereas an irregular dodecagon has unequal sides and angles. You can find a regular dodecagon's area with the equation, area = 12 * side measurement squared / 4 * tangent (pi /12), and a irregular dodecagon's area by dividing the polygon into smaller shapes.
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Instructions
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Regular
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1
Divide the math constant pi, which is approximately 3.142, by 12, the number of sides. Pi divided by 12 equals approximately 0.2618.
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2
Calculate the tangent measured in radians of the product from Step 1 on your calculator, then multiply the tangent by 4. The tangent in radians of 0.2618 is approximately 0.2679, which when multiplied by 4 equals 1.0716.
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3
Measure one side of the dodecagon and then square the measurement. For this example, allow a side to measure 4 inches, and 4 inches squared is 16 square inches.
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4
Multiply the squared side length by 12, the number of sides. In this example, 16 square inches multiplied by 12 equals 192 square inches.
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5
Divide the amount of square inches by the quotient from Step 2. Concluding this example, 192 square inches divided by 1.0716 equals approximately 179.1713 square inches.
Irregular
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6
Divide the dodecagon area into triangles. For this example, the dodecagon divides into 10 triangles.
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7
Find the measurements of the individual triangles. In this example, the triangle's measurements are as follow: triangle 1 has a 4-inch base and a 5-inches height; triangle 2 has a 3-inch base and a 4-inch height; triangle 3 has a 5-inch base and a 5-inch height; triangle 4-inch base and a 3-inch height; triangle 5 has a 5-inch base and 6-inch height; triangle 6 has a 6-inch base and a 5-inch height; triangle 7 has a 3-inch base and a 2-inch height; triangle 8 has a 2-inch base and a 3-inch height; triangle 9 has a 2-inch base and a 2-inch height; and triangle 10 has 2-inch base and a 1-inch height.
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8
Calculate the areas of the individual triangles. The area of a triangle can be found with the formula area = 1/2 *base * height. For this example, the triangles' areas are as follow: 10 square inches, 6 square inches, 12.5 square inches, 6 square inches, 15 square inches, 15 square inches, 3 square inches, 3 square inches, 2 square inches and 1 square inch.
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9
Add the triangles' areas together to calculate the area of the dodecagon. Concluding this example, adding the areas from Step 3 results in 73.5 square inches.
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