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:

 $\displaystyle A=width\times length$

$\displaystyle A=20\times15=300$

The area of the two right triangles can be found using the formula: 

$\displaystyle A=\frac{base\times height}{2}$

$\displaystyle A=\frac{10\times 8}{2}=\frac{80}{2}=40$

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:

$\displaystyle A=300+40+40=380$

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:

 $\displaystyle A=width\times length$

$\displaystyle A=26\times16=416$

The area of the two right triangles can be found using the formula: 

$\displaystyle A=\frac{base\times height}{2}$

$\displaystyle A=\frac{13\times 12}{2}=\frac{156}{2}=78$

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:

$\displaystyle A=416+78+78=572$

By definition a regular pentagon must have $\displaystyle 5$ equal sides and $\displaystyle 5$ equivalent interior angles. Since we are told that this pentagon has a side length of $\displaystyle 9$ inches, all of the sides must have a length of $\displaystyle 9$ 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 $\displaystyle 5$ equivalent interior triangles. Each triangle will have a base of $\displaystyle 9$ and a height of $\displaystyle 6.2$. 

The area of this pentagon can be found by applying the area of a triangle formula:

$\displaystyle A=\frac{base\times height}{2}$

$\displaystyle A=\frac{9\times 6.2}{2}=\frac{55.8}{2}=27.9$ 

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:

$\displaystyle 27.9\times5=139.5$ 

By definition a regular pentagon must have $\displaystyle 5$ equal sides and $\displaystyle 5$ 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 $\displaystyle 5$ equivalent interior triangles. Each triangle will have a base of $\displaystyle 14$ and a height of $\displaystyle 9.6$. 

The area of this pentagon can be found by applying the area of a triangle formula: 

$\displaystyle A=\frac{base\times height}{2}$


$\displaystyle A=\frac{14\times 9.6}{2}=\frac{134.4}{2}=67.2$

Note: $\displaystyle 67.2$ is only the measurement for one of the five interior triangles. Thus, the final solution is: 

$\displaystyle 67.2\times5=336$

To solve this problem, first work backwards using the perimeter formula for a regular pentagon: 

$\displaystyle p=5(s)$

$\displaystyle 60=5(s)$

$\displaystyle s=\frac{60}{5}=12$

Now you have enough information to find the area of this regular triangle. 
Note: a regular pentagon must have $\displaystyle 5$ equal sides and $\displaystyle 5$ 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 $\displaystyle 5$ equivalent interior triangles. Each triangle will have a base of $\displaystyle 12$ and a height of $\displaystyle 8.3$. 

The area of this pentagon can be found by applying the area of a triangle formula: 

$\displaystyle A=\frac{base\times height}{2}$

$\displaystyle A=\frac{8.3\times 12}{2}=\frac{99.6}{2}=49.8$

Thus, the area of the entire pentagon is:

$\displaystyle A=49.8\times 5=249$

By definition a regular pentagon must have $\displaystyle 5$ equal sides and $\displaystyle 5$ 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 $\displaystyle 5$ equivalent interior triangles. Each triangle will have a base of $\displaystyle 15$ and a height of $\displaystyle 10.3$. 

The area of this pentagon can be found by applying the area of a triangle formula: 

$\displaystyle A=\frac{base\times height}{2}$


$\displaystyle A=\frac{15\times 10.3}{2}=\frac{154.5}{2}=77.25$

Keep in mind that this is the area for only one of the five total interior triangles. 

The total area of the pentagon is:

$\displaystyle A=77.25\times 5=386.25$

To solve this problem, first work backwards using the perimeter formula for a regular pentagon: 

$\displaystyle p=5(s)$

$\displaystyle 50=5(s)$

$\displaystyle s=\frac{50}{5}=10$

Now you have enough information to find the area of this regular triangle. 
Note: a regular pentagon must have $\displaystyle 5$ equal sides and $\displaystyle 5$ 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 $\displaystyle 5$ equivalent interior triangles. Each triangle will have a base of $\displaystyle 10$ and a height of $\displaystyle 7$. 

The area of this pentagon can be found by applying the area of a triangle formula: 

$\displaystyle A=\frac{base\times height}{2}$

$\displaystyle A=\frac{10\times 7}{2}=\frac{70}{2}=35$

To find the total area of the pentagon multiply:

$\displaystyle 35\times5=175$

By definition a regular pentagon must have $\displaystyle 5$ equal sides and $\displaystyle 5$ 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 $\displaystyle 5$ equivalent interior triangles. Each triangle will have a base of $\displaystyle 25$ and a height of $\displaystyle 17.2$. 

The area of this pentagon can be found by applying the area of a triangle formula: 

$\displaystyle A=\frac{base\times height}{2}$


$\displaystyle A=\frac{25\times 17.2}{2}=\frac{430}{2}=215$

However, the total area of the pentagon is equal to: 

$\displaystyle 215\times 5= 1,075$

By definition a regular pentagon must have $\displaystyle 5$ equal sides and $\displaystyle 5$ 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 $\displaystyle 5$ equivalent interior triangles. Each triangle will have a base of $\displaystyle 7$ and a height of $\displaystyle 4.8$. 

The area of this pentagon can be found by applying the area of a triangle formula: 

$\displaystyle A=\frac{base\times height}{2}$


$\displaystyle A=\frac{7\times 4.8}{2}=\frac{33.6}{2}=16.8$

Note: $\displaystyle 16.8$ is only the measurement for one of the five interior triangles. Thus, the solution is: 

$\displaystyle 16.8\times5=84$

To solve this problem, first work backwards using the perimeter formula for a regular pentagon: 

$\displaystyle p=5(s)$

$\displaystyle 65=5(s)$

$\displaystyle s=\frac{65}{5}=13$

Now you have enough information to find the area of this regular triangle. 
Note: a regular pentagon must have $\displaystyle 5$ equal sides and $\displaystyle 5$ 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 $\displaystyle 5$ equivalent interior triangles. Each triangle will have a base of $\displaystyle 13$ and a height of $\displaystyle 8.9$. 

The area of this pentagon can be found by applying the area of a triangle formula: 

$\displaystyle A=\frac{base\times height}{2}$

$\displaystyle A=\frac{8.9\times 13}{2}=\frac{115.7}{2}=57.85$

Thus, the area of the entire pentagon is:

$\displaystyle A=57.85\times 5=289.25$