Calculating the perimeter of a polygon - GMAT Quantitative Reasoning
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What is the perimeter of a hexagon?
-
Each side measures 10 cm
-
The hexagon is regular.
What is the perimeter of a hexagon?
-
Each side measures 10 cm
-
The hexagon is regular.
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.
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.
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Note: Figure NOT drawn to scale
What is the perimeter of the above figure?
Assume all angles shown in the figure are right angles.
Note: Figure NOT drawn to scale
What is the perimeter of the above figure?
Assume all angles shown in the figure are right angles.
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.
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:
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What is the perimeter of a rectangle with a length of 
and a width of 
?
What is the perimeter of a rectangle with a length of
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:
The perimeter
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What is the perimeter of a right triangle with a base of 
and a height of 
?
What is the perimeter of a right triangle with a base of
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 
:
In order to find the perimeter
We could have also noted that
Now that we have all three side lengths, we can calculate
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What is the perimeter of an octagon with equal side lengths of 
each?
What is the perimeter of an octagon with equal side lengths of
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:
Starting with the knowledge that we are dealing with an octagon, an 8-sided figure, we calculate the perimeter
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is a pentagon with two sets of congruent sides and one side that is longer than all the others.
The smallest pair of congruent sides are 5 inches long each.
The other two congruent sides are 1.5 times bigger than the smallest sides.
The last side is twice the length of the smallest sides.
What is the perimeter of 
?
The smallest pair of congruent sides are 5 inches long each.
The other two congruent sides are 1.5 times bigger than the smallest sides.
The last side is twice the length of the smallest sides.
What is the perimeter of
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 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
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One side of a regular dodecagon has a length of 
. What is the perimeter of the polygon?
One side of a regular dodecagon has a length of
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:
A regular dodecagon is a polygon with twelve sides of equal length, so if one side has a length of
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