Q&A for How to Find the Area of a Regular Pentagon

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How do I find the perimeter of a pentagon when I'm only given the apothem?

Donagan

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The perimeter of a regular pentagon is the apothem multiplied by 7.267.

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Question

What would be the length of a side of a regular pentagon with a perimeter of 12.5?

Donagan

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Each side of a regular pentagon is one-fifth of the perimeter. So in this case, each side measures 12.5 / 5 = 2.5.

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I am struggling to find the length of one side of a pentagon; two sides are 0.9 meters, 2 other sides at 0.53 meters each.

Donagan

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There is no formula available for finding a side of an irregular pentagon.

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Is there any formula which uses only algebraic variables to find the area of a regular pentagon where only the length of side is provided? The formula should not use trigonometry.

Donagan

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No, the only way to do it is Method 2 above.

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If we have two pentgons, the area for small one is 29 and the length 4, then how do we find area for biggest one if the length is 12?

Donagan

Top Answerer

Assuming you're dealing with "regular" pentagons, you would set two ratios equal to each other. One ratio would be of the areas of the two pentagons (one of which is unknown), and the other ratio would be of the two side lengths (both of which are known). Solve the equation for the unknown area by cross-multiplying. Thus, 29 / x = 4 / 12, where x is the unknown area. Cross-multiply: (29)(12) = 4x. 348 = 4x, and x = 87.

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Question

How do I find the side of a regular pentagon if I'm given the area?

Donagan

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Use the formula in Method 3 above, and work backwards to solve for s.

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How do I find the area of a pentagon if it is irregular?

Community Answer

Break into triangles, then add. The polygon can be broken up into triangles by drawing all the diagonals from one of the vertices. If you know enough sides and angles to find the area of each, then you can simply add them up to find the total. Do not be afraid to draw extra lines anywhere if they will help find shapes you can solve.

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Question

How do I find the area of a regular pentagon with apothem of 12 inches?

Donagan

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As explained in the above article, the side length is needed in order to find a regular pentagon's area.

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How do I find the area of a pentagon if I know the perimeter?

Donagan

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Assuming a regular pentagon, divide the perimeter by 5 to get the length of each side, then use Method 2 above.

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How do I find the area of a regular pentagon with no side length or apothem given? Only one angle of a triangle is given, which is 72.

Donagan

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It's impossible to find the area if all you know is an angle.

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When I divide the pentagon into five triangles, are the triangles equilateral triangles?

Community Answer

No. Because all radii of a pentagon are equal, the triangles are isosceles but not necessarily equilateral.

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Question

If the surface area is 32, then what's the length of the sides?

Community Answer

If you're referring to a regular pentagon with a perimeter of 32, the length of each side is 32 / 5. In Method 3, the area of a pentagon is A = (5s²)/(4tan(36º)), from which you can find 5s² = Ax(4tan(36º)), so that s = √(Ax(4tan(36º))/5), and since tan(36º) = √(5-2√5), you can also use s = √(Ax(4√(5-2√5))/5). Use either formula to get the side of the pentagon to be s = 4.313. The first formula has less parentheses and square roots, and is easier to use.

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How do I find the surface area of my blender?

Community Answer

Find the height of the blender, then measure its width, multiply these and you will have your answer.

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How do I calculate the area of pentagon with an apothem of 7.04?

Community Answer

The apothem to side length ratio is around 0.688. You then find the side length by doing 7.04/0.688. From there, you can solve, because area = (5/2)*(side length)*(apothem).

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