How to find the area of a pentagon - Math
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What is the area of a regular pentagon with side length 
?
What is the area of a regular pentagon with side length
Tap to reveal answer
The area of a regular polygon can be solved using the following equation: 
.
To find the perimeterof the pentagon, we multiply the side length by five.
The apothem of a regular polygon (
= number of sides; 
= side length) is given by the equation below.
Pluggin in our numbers, we can solve for the apothem.
Finally, we can solve for the area.
The area of a regular polygon can be solved using the following equation:
To find the perimeterof the pentagon, we multiply the side length by five.
The apothem of a regular polygon (
Pluggin in our numbers, we can solve for the apothem.
Finally, we can solve for the area.
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Find the area of the following pentagon:
Find the area of the following pentagon:
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The formula for the area of of a pentagon is
.
Plugging in our values, we get:
The formula for the area of of a pentagon is
Plugging in our values, we get:
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Find the area of the following pentagon:
Find the area of the following pentagon:
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The formula for the area of of a pentagon is:
Plugging in our values, we get:
The formula for the area of of a pentagon is:
Plugging in our values, we get:
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A regular pentagon has a side length of 
inches and an apothem length of 
inches. Find the area of the pentagon.
A regular pentagon has a side length of
Tap to reveal answer
By definition a regular pentagon must have 
equal sides and 
equivalent interior angles. Since we are told that this pentagon has a side length of 
inches, all of the sides must have a length of 
inches. Additionally, the question provides the length of the apothem of the pentagon--which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into 
equivalent interior triangles. Each triangle will have a base of 
and a height of 
.
The area of this pentagon can be found by applying the area of a triangle formula:
Note: the area shown above is only the a measurement from one of the five total interior triangles. Thus, to find the total area of the pentagon multiply:
By definition a regular pentagon must have
The area of this pentagon can be found by applying the area of a triangle formula:
Note: the area shown above is only the a measurement from one of the five total interior triangles. Thus, to find the total area of the pentagon multiply:
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A regular pentagon has a side length of 
and an apothem length of 
. Find the area of the pentagon.
A regular pentagon has a side length of
Tap to reveal answer
By definition a regular pentagon must have equal sides and equivalent interior angles.
This question provides the length of the apothem of the pentagon--which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into equivalent interior triangles. Each triangle will have a base of 
and a height of 
.
The area of this pentagon can be found by applying the area of a triangle formula:
Note: 
is only the measurement for one of the five interior triangles. Thus, the final solution is:
By definition a regular pentagon must have
This question provides the length of the apothem of the pentagon--which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into
The area of this pentagon can be found by applying the area of a triangle formula:
Note:
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Find the area of the pentagon shown above.
Find the area of the pentagon shown above.
Tap to reveal answer
To find the area of this pentagon, divide the interior of the pentagon into a four-sided rectangle and two right triangles. The area of the bottom rectangle can be found using the formula:
The area of the two right triangles can be found using the formula:
Since there are two right triangles, the sum of both will equal the area of the entire triangular top portion of the pentagon.
Thus, the solution is:
To find the area of this pentagon, divide the interior of the pentagon into a four-sided rectangle and two right triangles. The area of the bottom rectangle can be found using the formula:
The area of the two right triangles can be found using the formula:
Since there are two right triangles, the sum of both will equal the area of the entire triangular top portion of the pentagon.
Thus, the solution is:
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A regular pentagon has a perimeter of 
yards and an apothem length of 
yards. Find the area of the pentagon.
A regular pentagon has a perimeter of
Tap to reveal answer
To solve this problem, first work backwards using the perimeter formula for a regular pentagon:
Now you have enough information to find the area of this regular triangle.
Note: a regular pentagon must have equal sides and equivalent interior angles.
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into equivalent interior triangles. Each triangle will have a base of 
and a height of 
.
The area of this pentagon can be found by applying the area of a triangle formula:
Thus, the area of the entire pentagon is:
To solve this problem, first work backwards using the perimeter formula for a regular pentagon:
Now you have enough information to find the area of this regular triangle.
Note: a regular pentagon must have
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into
The area of this pentagon can be found by applying the area of a triangle formula:
Thus, the area of the entire pentagon is:
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A regular pentagon has a side length of 
and an apothem length of 
. Find the area of the pentagon.
A regular pentagon has a side length of
Tap to reveal answer
By definition a regular pentagon must have equal sides and equivalent interior angles.
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into equivalent interior triangles. Each triangle will have a base of 
and a height of 
.
The area of this pentagon can be found by applying the area of a triangle formula:
Keep in mind that this is the area for only one of the five total interior triangles.
The total area of the pentagon is:
By definition a regular pentagon must have
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into
The area of this pentagon can be found by applying the area of a triangle formula:
Keep in mind that this is the area for only one of the five total interior triangles.
The total area of the pentagon is:
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A regular pentagon has a perimeter of 
and an apothem length of 
. Find the area of the pentagon.
A regular pentagon has a perimeter of
Tap to reveal answer
To solve this problem, first work backwards using the perimeter formula for a regular pentagon:
Now you have enough information to find the area of this regular triangle.
Note: a regular pentagon must have equal sides and equivalent interior angles.
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into equivalent interior triangles. Each triangle will have a base of 
and a height of 
.
The area of this pentagon can be found by applying the area of a triangle formula:
To find the total area of the pentagon multiply:
To solve this problem, first work backwards using the perimeter formula for a regular pentagon:
Now you have enough information to find the area of this regular triangle.
Note: a regular pentagon must have
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into
The area of this pentagon can be found by applying the area of a triangle formula:
To find the total area of the pentagon multiply:
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A regular pentagon has a side length of 
and an apothem length of 
. Find the area of the pentagon.
A regular pentagon has a side length of
Tap to reveal answer
By definition a regular pentagon must have equal sides and equivalent interior angles.
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into equivalent interior triangles. Each triangle will have a base of 
and a height of 
.
The area of this pentagon can be found by applying the area of a triangle formula:
However, the total area of the pentagon is equal to:
By definition a regular pentagon must have
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into
The area of this pentagon can be found by applying the area of a triangle formula:
However, the total area of the pentagon is equal to:
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Find the area of the pentagon shown above.
Find the area of the pentagon shown above.
Tap to reveal answer
To find the area of this pentagon, divide the interior of the pentagon into a four-sided rectangle and two right triangles. The area of the bottom rectangle can be found using the formula:
The area of the two right triangles can be found using the formula:
Since there are two right triangles, the sum of both will equal the area of the entire triangular top portion of the pentagon.
Thus, the solution is:
To find the area of this pentagon, divide the interior of the pentagon into a four-sided rectangle and two right triangles. The area of the bottom rectangle can be found using the formula:
The area of the two right triangles can be found using the formula:
Since there are two right triangles, the sum of both will equal the area of the entire triangular top portion of the pentagon.
Thus, the solution is:
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A regular pentagon has a side length of 
and an apothem length of 
. Find the area of the pentagon.
A regular pentagon has a side length of
Tap to reveal answer
By definition a regular pentagon must have equal sides and equivalent interior angles.
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into equivalent interior triangles. Each triangle will have a base of 
and a height of 
.
The area of this pentagon can be found by applying the area of a triangle formula:
Note: 
is only the measurement for one of the five interior triangles. Thus, the solution is:
By definition a regular pentagon must have
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into
The area of this pentagon can be found by applying the area of a triangle formula:
Note:
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A regular pentagon has a perimeter of 
and an apothem length of 
. Find the area of the pentagon.
A regular pentagon has a perimeter of
Tap to reveal answer
To solve this problem, first work backwards using the perimeter formula for a regular pentagon:
Now you have enough information to find the area of this regular triangle.
Note: a regular pentagon must have equal sides and equivalent interior angles.
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into equivalent interior triangles. Each triangle will have a base of 
and a height of 
.
The area of this pentagon can be found by applying the area of a triangle formula:
Thus, the area of the entire pentagon is:
To solve this problem, first work backwards using the perimeter formula for a regular pentagon:
Now you have enough information to find the area of this regular triangle.
Note: a regular pentagon must have
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into
The area of this pentagon can be found by applying the area of a triangle formula:
Thus, the area of the entire pentagon is:
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Find the area of the pentagon shown above.
Find the area of the pentagon shown above.
Tap to reveal answer
To find the area of this pentagon, divide the interior of the pentagon into a four-sided rectangle and two right triangles. The area of the bottom rectangle can be found using the formula:
The area of the two right triangles can be found using the formula:
Since there are two right triangles, the sum of both will equal the area of the entire triangular top portion of the pentagon.
Thus, the solution is:
To find the area of this pentagon, divide the interior of the pentagon into a four-sided rectangle and two right triangles. The area of the bottom rectangle can be found using the formula:
The area of the two right triangles can be found using the formula:
Since there are two right triangles, the sum of both will equal the area of the entire triangular top portion of the pentagon.
Thus, the solution is:
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A regular pentagon has a perimeter of 
and an apothem length of 
. Find the area of the pentagon.
A regular pentagon has a perimeter of
Tap to reveal answer
To solve this problem, first work backwards using the perimeter formula for a regular pentagon:
Now you have enough information to find the area of this regular triangle.
Note: a regular pentagon must have equal sides and equivalent interior angles.
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into equivalent interior triangles. Each triangle will have a base of 
and a height of 
.
The area of this pentagon can be found by applying the area of a triangle formula:
Thus, the area of the entire pentagon is:
To solve this problem, first work backwards using the perimeter formula for a regular pentagon:
Now you have enough information to find the area of this regular triangle.
Note: a regular pentagon must have
This question provides the length of the apothem of the pentagon—which is the length from the center of the pentagon to the center of a side. This information will allow us to divide the pentagon into
The area of this pentagon can be found by applying the area of a triangle formula:
Thus, the area of the entire pentagon is:
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Each side of this pentagon has a length of 
.
Solve for the area of the pentagon.
Each side of this pentagon has a length of
Solve for the area of the pentagon.
Tap to reveal answer
The formula for area of a pentagon is 
, with 
representing the length of one side and 
representing the apothem.
To find the apothem, we can convert our one pentagon into five triangles and solve for the height of the triangle:
Each of these triangles have angle measures of 
, with 
being the angle oriented around the vertex. This is because the polygon has been divided into five triangles and 
.
To solve for the apothem, we can use basic trigonometric ratios:
Now that we know the apothem length, we can plug in all our values to solve for area:
The formula for area of a pentagon is
To find the apothem, we can convert our one pentagon into five triangles and solve for the height of the triangle:
Each of these triangles have angle measures of
To solve for the apothem, we can use basic trigonometric ratios:
Now that we know the apothem length, we can plug in all our values to solve for area:
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Each side of this regular pentagon has a length of 
. Solve for the area of the pentagon. Round to the nearest tenth.
Each side of this regular pentagon has a length of
Tap to reveal answer
When given the value of one side of a regular pentagon, we can assume all sides to be of equal length and we can use this formula to calculate area:
For thi formula, 
represents the length of one side while 
represents the number of sides. Therefore, we would plug in the values as such:
When given the value of one side of a regular pentagon, we can assume all sides to be of equal length and we can use this formula to calculate area:
For thi formula,
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A regular pentagon has a side length of 
. Find the area rounded to the nearest tenth.
A regular pentagon has a side length of
Tap to reveal answer
We can use the following equation to solve for the area of a regular polygon with 
representing side length and 
representing number of sides:
We can use the following equation to solve for the area of a regular polygon with
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Find the area of the regular pentagon.
Find the area of the regular pentagon.
Tap to reveal answer
Recall that the area of regular polygons can be found using the following formula:
First, find the perimeter of the pentagon. Since it is a regular pentagon, we can use the following formula to find its perimeter:
Substitute in the length of the given side of the pentagon in order to find the perimeter.
Next, substitute in the given and calculated information to find the area of the pentagon.
Recall that the area of regular polygons can be found using the following formula:
First, find the perimeter of the pentagon. Since it is a regular pentagon, we can use the following formula to find its perimeter:
Substitute in the length of the given side of the pentagon in order to find the perimeter.
Next, substitute in the given and calculated information to find the area of the pentagon.
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Find the area of the regular pentagon.
Find the area of the regular pentagon.
Tap to reveal answer
Recall that the area of regular polygons can be found using the following formula:
First, find the perimeter of the pentagon. Since it is a regular pentagon, we can use the following formula to find its perimeter:
Substitute in the length of the given side of the pentagon in order to find the perimeter.
Next, substitute in the given and calculated information to find the area of the pentagon.
Recall that the area of regular polygons can be found using the following formula:
First, find the perimeter of the pentagon. Since it is a regular pentagon, we can use the following formula to find its perimeter:
Substitute in the length of the given side of the pentagon in order to find the perimeter.
Next, substitute in the given and calculated information to find the area of the pentagon.
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