# Area of Polygons

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How to find the area of trapezoids, hexagons, pentagons, and octagons?

• Trapezoid: Area = 1/2 x (sum of the bases) x height A trapezoid is a shape with two parallel sides and two non-parallel sides. To find the area of a trapezoid, we add the lengths of the two parallel sides (called the bases), then multiply by the height and divide by 2. For example, a trapezoid with a height of 4 units, a base of 6 units, and another base of 8 units has an area of 1/2 x (6 + 8) x 4 = 28 square units.

• Hexagon: Area = 3/2 x (side length) squared x square root of 3 A hexagon is a shape with six sides of equal length. To find the area of a regular hexagon, we multiply the square of the length of one side by 3/2, then multiply by the square root of 3. For example, a hexagon with a side length of 5 units has an area of 3/2 x 5^2 x square root of 3 ≈ 64.95 square units.

• Pentagon: Area = 1/4 x (square root of [5(5 + 2(square root of 5)))]) x side length squared A pentagon is a shape with five sides of equal length. To find the area of a regular pentagon, we use the formula above. For example, a pentagon with a side length of 7 units has an area of 1/4 x (square root of [5(5 + 2(square root of 5)))]) x 7^2 ≈ 84.3 square units.

• Octagon: Area = 2 x (1 + square root of 2) x side length squared An octagon is a shape with eight sides of equal length. To find the area of a regular octagon, we multiply the square of the length of one side by 2 times the quantity 1 plus the square root of 2. For example, an octagon with a side length of 9 units has an area of 2 x (1 + square root of 2) x 9^2 ≈ 305.36 square units.

I hope that helps you understand how to find the area of trapezoids, hexagons, pentagons, and octagons!