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.
Divide the math constant pi, which is approximately 3.142, by 12, the number of sides. Pi divided by 12 equals approximately 0.2618.
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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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.
Multiply the squared side length by 12, the number of sides. In this example, 16 square inches multiplied by 12 equals 192 square inches.
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.
Divide the dodecagon area into triangles. For this example, the dodecagon divides into 10 triangles.
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.
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.
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.