Calculating the perimeter of a polygon - GMAT Quantitative

This figure can be seen as a smaller rectangle cut out of a larger one; refer to the diagram below.

We can fill in the missing sidelengths using the fact that a rectangle has congruent opposite sides. Once this is done, we can add the lengths of the sides to get the perimeter:

feet.

The perimeter of any figure is the sum of the lengths of its sides. Since we have a rectangle with a length of and a width of , we know that there will be two sides of length and two sides of width . Therefore:

In order to find the perimeter of the right triangle, we need to know the lengths of each of its sides. While we are given two sides - the base and the height - we do not know the hypotenuse . There are two ways that we can find , the first of which is the direct application of the Pythagorean Theorem:

We could have also noted that is a common Pythagorean Triple and deduced the value of that way.

Now that we have all three side lengths, we can calculate :

Starting with the knowledge that we are dealing with an octagon, an 8-sided figure, we calculate the perimeter by adding the lengths of all 8 sides. Since we also know that each side measures , we can use multiplication:

A pentagon is a 5 sided shape. We are given that two sides are 5 inches each.

Side 1 = 5inches

Side 2 = 5 inches

The next two sides are each 1.5 times bigger than the smallest two sides.

Side 3 =Side 4= 7.5 inches

The last side is twice the size of the smallest side,

Side 5 =10 inches

Add them all up for our perimeter:

5+5+7.5+7.5+10=35 inches long

A regular dodecagon is a polygon with twelve sides of equal length, so if one side has a length of , then the perimeter will be equal to twelve times the length of that one side. This gives us:

The perimeter is the sum of the measures of the sidelengths.

Knowing that the hexagon is regular only tells you the six sides are congruent; without the measure of any side, this does not help you.

Knowing only that each of the six sides measures 10 cm is by itself enough to calculate the perimeter to be

.

The answer is that Statement 1 is sufficient, but not Statement 2.

This figure can be seen as a smaller rectangle cut out of a larger one; refer to the diagram below.

We can fill in the missing sidelengths using the fact that a rectangle has congruent opposite sides. Once this is done, we can add the lengths of the sides to get the perimeter:

feet.

The perimeter of any figure is the sum of the lengths of its sides. Since we have a rectangle with a length of and a width of , we know that there will be two sides of length and two sides of width . Therefore:

In order to find the perimeter of the right triangle, we need to know the lengths of each of its sides. While we are given two sides - the base and the height - we do not know the hypotenuse . There are two ways that we can find , the first of which is the direct application of the Pythagorean Theorem:

We could have also noted that is a common Pythagorean Triple and deduced the value of that way.

Now that we have all three side lengths, we can calculate :

Starting with the knowledge that we are dealing with an octagon, an 8-sided figure, we calculate the perimeter by adding the lengths of all 8 sides. Since we also know that each side measures , we can use multiplication:

A pentagon is a 5 sided shape. We are given that two sides are 5 inches each.

Side 1 = 5inches

Side 2 = 5 inches

The next two sides are each 1.5 times bigger than the smallest two sides.

Side 3 =Side 4= 7.5 inches

The last side is twice the size of the smallest side,

Side 5 =10 inches

Add them all up for our perimeter:

5+5+7.5+7.5+10=35 inches long

A regular dodecagon is a polygon with twelve sides of equal length, so if one side has a length of , then the perimeter will be equal to twelve times the length of that one side. This gives us:

The perimeter is the sum of the measures of the sidelengths.

Knowing that the hexagon is regular only tells you the six sides are congruent; without the measure of any side, this does not help you.

Knowing only that each of the six sides measures 10 cm is by itself enough to calculate the perimeter to be

.

The answer is that Statement 1 is sufficient, but not Statement 2.

This figure can be seen as a smaller rectangle cut out of a larger one; refer to the diagram below.

We can fill in the missing sidelengths using the fact that a rectangle has congruent opposite sides. Once this is done, we can add the lengths of the sides to get the perimeter:

feet.

The perimeter of any figure is the sum of the lengths of its sides. Since we have a rectangle with a length of and a width of , we know that there will be two sides of length and two sides of width . Therefore:

In order to find the perimeter of the right triangle, we need to know the lengths of each of its sides. While we are given two sides - the base and the height - we do not know the hypotenuse . There are two ways that we can find , the first of which is the direct application of the Pythagorean Theorem:

We could have also noted that is a common Pythagorean Triple and deduced the value of that way.

Now that we have all three side lengths, we can calculate :

Starting with the knowledge that we are dealing with an octagon, an 8-sided figure, we calculate the perimeter by adding the lengths of all 8 sides. Since we also know that each side measures , we can use multiplication:

A pentagon is a 5 sided shape. We are given that two sides are 5 inches each.

Side 1 = 5inches

Side 2 = 5 inches

The next two sides are each 1.5 times bigger than the smallest two sides.

Side 3 =Side 4= 7.5 inches

The last side is twice the size of the smallest side,

Side 5 =10 inches

Add them all up for our perimeter:

5+5+7.5+7.5+10=35 inches long