Math and Arithmetic
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# How do you calculate the area of a pentagon?

394041 ###### 2013-03-25 23:20:59

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:
1. The lines must not cross.
2. The lines must not connect adjacent verticies.
3. The lines must be contained completely inside the pentagon.
Once the three triangle are determined then the area of the pentagon can be calculated as the sum of the areas of the three triangles.
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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## Related Questions 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. 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 Given only the information in the question, there is no option but to measure the pentagon at the base and calculate its area.  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.  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. The area (A) formula of a regular pentagon of side length (a) is: A = [a2x(25+10x51/2)1/2]/4 See the why in the development of such formula in the weblink below. A pentagon is a 2D shape. Volume and Surface Area is only found in 3D shapes. regular pentagon area of 12 000 m2 and an apothem of 40 m regular pentagon area of 12 000 m2 and an apothem of 40 m need to figure it out from area 12000 m2 The boy had to find the area and perimeter of the pentagon. The Pentagon has a total parking lot area of 67 acres. To find the area, first divide the shape into regular, simple shapes. Then use formulas to find the area of the smaller, regular shapes. Lastly, add up all the smaller areas to find the area of the original shape. Since the question does not say so, you may not assume that the pentagon is regular. One way to find the area is to select any point inside the pentagon and join it to each of the vertices. This will divide the pentagon into 5 triangles. You can then measure the sides of each triangle and thereby calculate its area. Then sum the areas of the triangles. You could also select one side in each triangle as the base and then draw and measure the perpendicular distance to the opposite vertex. That is another way to find the area of each triangle. There are other methods, too. To find the perimeter you will need to measure the length of each side of the pentagon and add these lengths together. you can't do this because it is a 2-D figure in order to find Surface Area you need a 3-D figure but you can find the area of a pentagon By adding the lengths of the 5 sides together.  A regular pentagon has five (5) equilateral triangles within it. Find the area of each triangle (1/2bh where b is the base of the triangle or the length of a side of the pentagon, and h is the height of the triangle or the apothem of the pentagon) and multiply the area of the triangle times five (5). The side lengths of a pentagon do not provide enough information to determine its exact shape and therefore its area.The side lengths of a pentagon do not provide enough information to determine its exact shape and therefore its area.The side lengths of a pentagon do not provide enough information to determine its exact shape and therefore its area.The side lengths of a pentagon do not provide enough information to determine its exact shape and therefore its area. ###### Math and ArithmeticLawn CareAreaGeometryHigh School ArchitectureExample SentencesLearning TheoriesMathematical FinanceFootball Field MeasurementsHobbies & Collectibles Copyright © 2020 Multiply Media, LLC. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.