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There are many different types of pentagons, and many different ways to calculate the area.

The General CaseAll pentagons can be subdivided into three triangles by drawing two line segments between pairs of pentagon vertices. There are three conditions that must be met when creating the two lines:- The lines must not cross.
- The lines must not connect adjacent verticies.
- The lines must be contained completely inside the pentagon.

The Regular PentagonA regular pentagon has five sides of the same length. Also, the interior angles are equivalent In this case the area of the pentagon can be calculated from the side length.

The approximately correct formula (s = side length):

A = s * s * 1.720477401. Put the word 'approximately' into context. If the length of a side is accurate to 2 decimal places, then using the factor of 1.72 will be accurate enough for you; using the 9 decimal places will not increase the accuracy of your answer beyond 2 decimal places. If you know the length of a side to an accuracy of 9 decimal places, the above factor will do the trick. But how often do you need accuracy to that degree? The 'exactly correct' solution below is exactly correct only in theory. When you plug real numbers in, your answer can be no closer to correct than the numbers you enter. So save yourself a lot of trouble and use the factor above.

The exactly correct formula (s = side length, sqrt means square root):

A = s2 * 1/4 sqrt [(25 +10 (sqrt5)]

The formula is derived at the link below.

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Q: How do you calculate the area of a pentagon?

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That depends on the size of the pentagon, and whether it is regular or not. In general, you can divide the pentagon into three triangles, and calculate the area of each triangle separately.

The simplest way is to divide the pentagon into three triangles, calculate the area of each of them and sum the answers.

divide the pentagon into 5 equilateral triangles, and calculate their area. (base times height divided by 2) and when you have your answer, multiply it by 5.

Given only the information in the question, there is no option but to measure the pentagon at the base and calculate its area.

Area(pentagon)=s2(1.7)

V = (1/3) (area of the base) (height) Area of a pentagon = 1/2 x apothem length x 5 x length of a side of the pentagonthe apothem is the perpendicular distance from the center of the pentagon to the side of the pentagon

If 6 is the side of a regular pentagon, the area is 61.937

The area of a pentagon of side length t is given by the formula t2 (sqrt 25 + 10 (sqrt 5)) / 4, or 5t2 tan (54o) / 4. In this case, a pentagon with one side of 10cm has an area of 102 (sqrt 25 + 10 (sqrt 5)) / 4 = 172.05 cm2 (accurate to two decimal places).

You didn't say it was a regular pentagon. For an arbitrary pentagon, you would calculate its area as you would for any polygon: divide it up into triangles, and add up the areas of the triangle. The area of a triangle is 1/2 times the base times the height, the height being the length of the perpendicular dropped to the base from the opposite vertex.

The only general way is to divide the pentagon into three triangles, calculate the areas of the triangles and add them together.

Oh yes, it most definitely will. They're equal.

The area of a regular pentagon with a radius of 7 is 10.1716. If the radius was 5, the area would be 7.26543.

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