# How do you calculate the area of a pentagon?

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

### The General Case

All 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 Pentagon

A 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.

### What is the formula for measuring the area of a pentagon?

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.

### How do you find the area and perimeter of a pentagon?

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…

### The apothem of a regular pentagon is 10.8 centimeters. What is the length of a side of the pentagon?

### The area of a regular pentagon is 600 cm Calculate the length of one side of the pentagon?

Area is not measured in centimeter units. It may be guessed that the question should have indicated the area in square centimeters. The area of a regular pentagon is given as: A = s * s * sqr(25 + 10*(sqr(5)) / 4 Solve for s: s = 2 * sqr (A / sqr(25 + 10*(sqr(5))) Insert the area of 600 square centimters: s = 2 * sqr (600 cm*cm / sqr(25 + 10*(sqr(5))) s =…

### What is the area of a regular pentagon with a side length of ten units?

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).

### What is the area of 8ft 4ft 4ft 4ft 5ft?

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…

### What is the area of a regular pentagon if each side is 8 meters the apothem is 6 meters and the radius is 7 meters?

== == The question does not make sense because the numbers are not consistent. It is a bit like asking the area of a circle if the radius is 6 and the diameter is 8. A circle's diameter is constrained to be twice the size of the radius. Similarly, the apothem of the specified pentagon is constrained to be a particular size and the apothem size is not 6. Also, a pentagon does not have…

### What is the demsion of the inner wall on the pentagon?

knowing that the outer wall is 921 feet and using A=(half)(apothem)(perimeter) you can determine the inside walls to be about 338 feet ... check my math though! if that be the case, then the inside pentagon has an area of 4.5 acres (use trig and formula above) ... google it and the Pentagon has an area of 29 acres ... 29+4.5 and you get 33.5 which is the are of a pentagon with side 921…

### What is the formula for finding area of a pentagon?

[ONLY WORKS FOR REGULAR PENTAGONS] I don't the exact formula, BUT, from what I learned in Geometry last year, I remember that if you have the radius from the center perpendicular to a side [for height] and if you have the length of the side of the pentagon, you can use a simple 1/2 times base time height to get 1/5th of the area. Then you just take that and multiply it by 5 to…

### How do you calculate the square feet of a space 50 ft x13 ft x 30 ft x 25 ft x 8 ft?

You cannot. Square feet is a measure of area and has two dimensions: lngth and breadth. The information provided in the question indicates an object in 5-dimensional hyperspace. Even assuming these were the sides of a pentagon, it would not be possible to answer the question. A pentagon is not a rigid figure and so information about its side lengths is not enough to determine its area. This is in the same way that a…

### Introduce pentagon in one paragraph in math?

A pentagon is a plane area which is enclosed by five straight lines. It is, therefore, a polygon. The sum of the five interior angles of a pentagon sum to 540 degrees and so, each interior angle of a regular pentagon measures 108 degrees. A pentagon has five diagonals. It can have none of five axes of symmetry.