# How to find the area of a decagon

By | 11.07.2021 Area of a Decagon Calculator

If you know the length of the perimeter in a decagon and the apothem, you can calculate its area using the following formula: area = p ? a 2 area = p ? a 2. A decagon with side length 5 cm has area of = 5/2 (25)v5 + 2v5 = cm 2.

The area of a decagon can be calculated using the following formula: if you know the perimeter and the apothem. If you know the length of the how to clean car upholstry in a decagon and the apothem, you can calculate its area using the following formula:. Vincular de regreso es opcional pero bienvenido. If you know the length of the perimeter in a decagon and the area, you can calculate its apothem using the following formula:.

A decagon is a plane geometric shape or polygon of 10 sides. It also has 10 angles and 10 vertices. The decagon can be regular or irregular. A regular decagon has all 10 sides of equal length and equal distance from the center. It looks very symmetrical.

All regular decagons look the same. An irregular decagon on the other hand can have sides of different shapes and angles.

There is a virtually infinite amount of variations for an irregular decagon, so that they can all look very different from each other. Despite these differences, they will always have 10 sides.

It is the space of the internal surface in a figure, it is limited for the perimeter. Also, the area can be calculated in a plane of how to find the area of a decagon dimensions. It is a representation of a rule or a general principle using letters. AlgebraA. Baldor When describing formulas in plural, it is also valid to say "formulae".

You are allowed to use our calculators in any project as long what is an airless paint sprayer you give attribution. Perimeter and Apothem Length. Area result. Calculate Reset. Perimeter and Area Length. Apothem result.

Clearing the Apothem

How to Calculate Area of decagon? Area of decagon calculator uses area = (5/2)*(Side ^2)*(sqrt (5+2* sqrt (5))) to calculate the Area, The Area of decagon formula is defined as the area covered by the ten sides and vertices of a decagon. Jul 24,  · This Area of a Decagon formula, (A decagon = 5 / 2 • v(5+2v5) • s 2), computes the area of a regular decagon, a polygon with 10 equal sides of length (s). Regular Decagon. Inputs. Choose your length units (e.g. feet, meters or even angstrom or light-years), and then enter the following: s - the length of the sides of the decagon. Finding the area of each trapezoid and adding those values together will result in the decagon's area. You can find the area of a trapezoid by adding the two base distances together then multiplying by the height and finally dividing by two.

Last Updated: April 1, References. To create this article, 25 people, some anonymous, worked to edit and improve it over time. This article has been viewed , times. Learn more A pentagon is a polygon with five straight sides. Almost all problems you'll find in math class will cover regular pentagons, with five equal sides.

There are two common ways to find the area, depending on how much information you have. To find the area of a regular pentagon with 5 equal sides, first get the length of a side and the apothem, which is the line from the center of the pentagon to a side that intersects the side at a degree angle. Then draw 5 lines from the center, 1 to each corner, so you have 5 triangles. For more on finding the area of a regular pentagon, including using formulas if you only know the length of a side or the radius, read on!

Related Articles. Article Summary. Method 1 of Start with the side length and apothem. This method works for regular pentagons, with five equal sides. Besides the side length, you'll need the "apothem" of the pentagon. Don't confuse the apothem with the radius, which touches a corner vertex instead of a midpoint.

If you only know the side length and radius, skip down to the next method instead. We'll use an example pentagon with side length 3 units and apothem 2 units. Divide the pentagon into five triangles. Draw five lines from the center of the pentagon, leading to each vertex corner. You now have five triangles. Calculate the area of a triangle. Each triangle has a base equal to the side of the pentagon. It also has a height equal to the pentagon's apothem. Remember, the height of a triangle runs from a vertex to the opposite side, at a right angle.

Multiply by five to find the total area. We've divided the pentagon into five equal triangles. To find the total area, just multiply the area of one triangle by five. Method 2 of Start with just the side length. This method only works for regular pentagons, which have five sides of equal length. In this example, we'll use a pentagon with side length 7 units. Draw a line from the center of the pentagon to any vertex. Repeat this for every vertex. You now have five triangles, each the same size.

Divide a triangle in half. Draw a line from the center of the pentagon to the base of one triangle. Label one of the smaller triangles. Calculate the height of the triangle. The height of this triangle is the side at right angles to the pentagon's edge, leading to the center.

We can use beginning trigonometry to find the length of this side:  X Research source In a right-angle triangle, the tangent of an angle equals the length of the opposite side, divided by the length of the adjacent side. Find the area of the triangle. Now that you know the height, plug in these values to find the area of your small triangle. Multiply to find the area of the pentagon. To find the total area, multiply the area of the smaller triangle by Method 3 of Use the perimeter and apothem.

The apothem is a line from the center of a pentagon, that hits a side at a right angle. Use the side length. Choose a formula that uses radius only. You can even find the area if you only know the radius. The perimeter of a regular pentagon is the apothem multiplied by 7. Not Helpful 33 Helpful What would be the length of a side of a regular pentagon with a perimeter of Each side of a regular pentagon is one-fifth of the perimeter. So in this case, each side measures Not Helpful 66 Helpful I am struggling to find the length of one side of a pentagon; two sides are 0.

There is no formula available for finding a side of an irregular pentagon. Not Helpful 55 Helpful 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. Not Helpful 32 Helpful Not Helpful 37 Helpful 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? 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. Not Helpful 46 Helpful Use the formula in Method 3 above, and work backwards to solve for s. Not Helpful 35 Helpful 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. Not Helpful 31 Helpful As explained in the above article, the side length is needed in order to find a regular pentagon's area.

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