Pentagons - ISEE Upper Level Quantitative Reasoning

A pentagon has 5 equal sides. We know the formula to find perimeter of a pentagon is

where a is the length of one side of the pentagon. Now, we know the total perimeter is 85in. Knowing this, we will substitute into the formula. We get

Therefore, the length of one side of the pentagon is 17in.

The angles of a pentagon measure a total of . From the information, we know that:

If , then

The angles of a pentagon measure a total of . If we let the unknown angle measure be , then from this information:

Since an angle measure cannot be negative, this pentagon cannot exist.

The angles of a pentagon measure a total of . From the information, we know:

If , then the above becomes:

The sum of the interior angles of a pentagon can be determined by the following equation, where is the number of sides:

Therefore:

The angles of a pentagon measure a total of . From the information, we know that:

If , then

The angles of a pentagon measure a total of . If we let the unknown angle measure be , then from this information:

Since an angle measure cannot be negative, this pentagon cannot exist.

The angles of a pentagon measure a total of . From the information, we know:

If , then the above becomes:

The sum of the interior angles of a pentagon can be determined by the following equation, where is the number of sides:

Therefore:

In a pentagon in which all angles are equal, all sides will also be equal; therefore, the length of one side can be found by dividing the perimeter by 5 (the number of sides in a pentagon). Given that , the sum of 2 of the sides will be

A pentagon has 5 equal sides. We know the formula to find perimeter of a pentagon is

where a is the length of one side of the pentagon. Now, we know the total perimeter is 85in. Knowing this, we will substitute into the formula. We get

Therefore, the length of one side of the pentagon is 17in.

In a pentagon in which all angles are equal, all sides will also be equal; therefore, the length of one side can be found by dividing the perimeter by 5 (the number of sides in a pentagon). Given that , the sum of 2 of the sides will be

A pentagon has 5 equal sides. We know the formula to find perimeter of a pentagon is

where a is the length of one side of the pentagon. Now, we know the total perimeter is 85in. Knowing this, we will substitute into the formula. We get

Therefore, the length of one side of the pentagon is 17in.

To find the perimeter of a pentagon, we will use the following formula:

where a is the length of one side of the pentagon.

Now, we know the length of one side of the pentagon is 12in.

Knowing this, we can substitute into the formula. We get

A pentagon has 5 sides. To find the perimeter, we will use the following formula:

where a is the length of a side of the pentagon.

Now, we know the length of a side of the pentagon is 21in.

Knowing this, we will substitute into the formula. We get

To find the perimeter of a pentagon, we will use the following formula:

where a is the length of one side of the pentagon. Because a pentagon has 5 equal sides, we can use any side in the formula.

So, we know the length of one side of the pentagon is 15cm. So, we can substitute. We get

A pentagon has 5 equal sides. To find the perimeter of a pentagon, we will use the following formula:

where a is the length of one side of the pentagon.

Now, we know a side of the pentagon has a length of 9in. So, we get

To find the perimeter of a pentagon, we will use the following formula:

where a is the length of one side of the pentagon.

Now, we know the length of one side of the pentagon is 11in.

Knowing this, we can substitute into the formula. We get

The angles of a pentagon measure a total of . From the information, we know that:

If , then