Perimeter and Sides - GED Math
Card 1 of 100
The above figure is a regular octagon. Give its perimeter in yards.
The above figure is a regular octagon. Give its perimeter in yards.
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A regular octagon has eight sides of equal length, so multiply the length of one side by eight:
feet.
Divide by three to get the equivalent in yards:
yards.
A regular octagon has eight sides of equal length, so multiply the length of one side by eight:
Divide by three to get the equivalent in yards:
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Identify the above polygon.
Identify the above polygon.
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A polygon with eight sides is called an octagon.
A polygon with eight sides is called an octagon.
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Refer to the above figure.
Which of the following is not a valid alternative name for Polygon 
?
Refer to the above figure.
Which of the following is not a valid alternative name for Polygon
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In naming a polygon, the vertices must be written in the order in which they are positioned, going either clockwise or counterclockwise. Of the four choices, only Polygon 
violates this convention, since 
and 
are not adjacent vertices (nor are 
and 
).
In naming a polygon, the vertices must be written in the order in which they are positioned, going either clockwise or counterclockwise. Of the four choices, only Polygon
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Refer to the above figure. All angles shown are right angles.
What is the perimeter of the figure?
Refer to the above figure. All angles shown are right angles.
What is the perimeter of the figure?
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The figure can be viewed as the composite of rectangles. As such, we can take advantage of the fact that opposite sides of a rectangle have the same length, as follows:
Now that the missing sidelengths are known, we can add the sidelengths to find the perimeter:
The figure can be viewed as the composite of rectangles. As such, we can take advantage of the fact that opposite sides of a rectangle have the same length, as follows:
Now that the missing sidelengths are known, we can add the sidelengths to find the perimeter:
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Refer to the above figure.
Which of the following segments is a diagonal of Pentagon 
?
Refer to the above figure.
Which of the following segments is a diagonal of Pentagon
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A diagonal of a polygon is a segment whose endpoints are nonconsecutive vertices of the polygon. Of the four choices, only 
fits this description.
A diagonal of a polygon is a segment whose endpoints are nonconsecutive vertices of the polygon. Of the four choices, only
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Classify the above polygon.
Classify the above polygon.
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A polygon with eight sides is called an octagon.
A polygon with eight sides is called an octagon.
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Hexagon 
is regular. If diagonals 
and 
are constructed, which of the following classifications applies to Quadrilateral 
?
I) Rectangle
II) Rhombus
III) Square
IV) Trapezoid
Hexagon
I) Rectangle
II) Rhombus
III) Square
IV) Trapezoid
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The figure described is below.
Since the hexagon is regular, its sides are congruent, and its angles each have measure 
.
Also, each of the triangles are isosceles, and their acute angles measure 
each. This means that each of the four angles of Quadrilateral measures 
, so Quadrilateral is a rectangle. However, not all sides are congruent, so it is not a rhombus. Also, since it is a rectangle, it cannot be a trapezoid.
The correct response is I only.
The figure described is below.
Since the hexagon is regular, its sides are congruent, and its angles each have measure
Also, each of the triangles are isosceles, and their acute angles measure
The correct response is I only.
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Classify the above polygon.
Classify the above polygon.
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A polygon with six sides is called a hexagon.
A polygon with six sides is called a hexagon.
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What is the perimeter of a semicircle with an area of 
?
What is the perimeter of a semicircle with an area of
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Write the formula for the area of a semicircle.
Substitute the area.
Multiply by 2, and divide by pi on both sides.
The equation becomes:
Square root both sides and factor the right side.
The diameter is double the radius.
The circumference is half the circumference of a full circle.
The perimeter is the sum of the diameter and the half circumference.
The answer is: 
Write the formula for the area of a semicircle.
Substitute the area.
Multiply by 2, and divide by pi on both sides.
The equation becomes:
Square root both sides and factor the right side.
The diameter is double the radius.
The circumference is half the circumference of a full circle.
The perimeter is the sum of the diameter and the half circumference.
The answer is:
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A hexagon has a perimeter of 90in. Find the length of one side.
A hexagon has a perimeter of 90in. Find the length of one side.
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A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:
where a is the length of any side. Now, to find the length of one side, we will solve for a.
We know the perimeter of the hexagon is 90in. So, we will substitute and solve for a. We get
Therefore, the length of one side of the hexagon is 15in.
A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:
where a is the length of any side. Now, to find the length of one side, we will solve for a.
We know the perimeter of the hexagon is 90in. So, we will substitute and solve for a. We get
Therefore, the length of one side of the hexagon is 15in.
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A hexagon has a perimeter of 138cm. Find the length of one side.
A hexagon has a perimeter of 138cm. Find the length of one side.
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A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is
where a is the length of any side. To find the length of one side, we solve for a.
Now, we know the perimeter of the hexagon is 138cm. So, we can substitute and solve for a. We get
Therefore, the length of one side of the hexagon is 23cm.
A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is
where a is the length of any side. To find the length of one side, we solve for a.
Now, we know the perimeter of the hexagon is 138cm. So, we can substitute and solve for a. We get
Therefore, the length of one side of the hexagon is 23cm.
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A hexagon has a perimeter of 126in. Find the length of one side.
A hexagon has a perimeter of 126in. Find the length of one side.
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A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:
where a is the length of any side. Now, to find the length of one side, we will solve for a.
We know the perimeter of the hexagon is 126in. So, we will substitute and solve for a. We get
Therefore, the length of one side of the hexagon is 21in.
A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is:
where a is the length of any side. Now, to find the length of one side, we will solve for a.
We know the perimeter of the hexagon is 126in. So, we will substitute and solve for a. We get
Therefore, the length of one side of the hexagon is 21in.
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A hexagon has a perimeter of 198cm. Find the length of one side.
A hexagon has a perimeter of 198cm. Find the length of one side.
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A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is
where a is the length of any side. To find the length of one side, we solve for a.
Now, we know the perimeter of the hexagon is 198cm. So, we can substitute and solve for a. We get
Therefore, the length of one side of the hexagon is 33cm.
A hexagon has 6 equal sides. The formula to find perimeter of a hexagon is
where a is the length of any side. To find the length of one side, we solve for a.
Now, we know the perimeter of the hexagon is 198cm. So, we can substitute and solve for a. We get
Therefore, the length of one side of the hexagon is 33cm.
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Figure NOT drawn to scale.
Refer to the above figure. Every angle shown is a right angle.
Give its perimeter.
Figure NOT drawn to scale.
Refer to the above figure. Every angle shown is a right angle.
Give its perimeter.
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Examine the bottom figure, in which the bottom two sides have been connected. Note that the figure is now a rectangle cut out of a rectangle, and, since the opposite sides of a rectangle have the same length, we can fill in some of the side lengths as shown:
Three of the sides are of unknown length, but it is not necessary to know the values. Since opposite sides of a rectangle are of the same length, it can be deduced that
.
The perimeter of the figure is equal to the sum of the lengths of its sides, which is
Substituting 100 for 
:
Examine the bottom figure, in which the bottom two sides have been connected. Note that the figure is now a rectangle cut out of a rectangle, and, since the opposite sides of a rectangle have the same length, we can fill in some of the side lengths as shown:
Three of the sides are of unknown length, but it is not necessary to know the values. Since opposite sides of a rectangle are of the same length, it can be deduced that
The perimeter of the figure is equal to the sum of the lengths of its sides, which is
Substituting 100 for
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What is the perimeter of a semicircle with a radius of 4?
What is the perimeter of a semicircle with a radius of 4?
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The semicircle perimeter will include half the circumference of a regular circle as well as the diameter.
Given the radius, we can first determine the circumference of the half circle.
The diameter is double the radius, or 
.
Sum the circumference and the diameter to get the perimeter.
The answer is: 
The semicircle perimeter will include half the circumference of a regular circle as well as the diameter.
Given the radius, we can first determine the circumference of the half circle.
The diameter is double the radius, or
Sum the circumference and the diameter to get the perimeter.
The answer is:
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Find the perimeter of a hexagon with a side of length 9cm.
Find the perimeter of a hexagon with a side of length 9cm.
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To find the perimeter of a hexagon, we will use the following formula:
where a is any side of the hexagon. Because a hexagon has 6 equal sides, we can use any of them in the formula.
Now, we know the hexagon has a side of 9cm. So, we can substitute. We get
To find the perimeter of a hexagon, we will use the following formula:
where a is any side of the hexagon. Because a hexagon has 6 equal sides, we can use any of them in the formula.
Now, we know the hexagon has a side of 9cm. So, we can substitute. We get
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Find the perimeter of a pentagon with a side of length 8in.
Find the perimeter of a pentagon with a side of length 8in.
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To find the perimeter of a pentagon, we will use the following formula:
where a is the length of any side of the pentagon. Because a pentagon has 5 equal sides, we can use any of those sides in the formula.
Now, we know the pentagon has a side of 8in. So, we can substitute. We get
To find the perimeter of a pentagon, we will use the following formula:
where a is the length of any side of the pentagon. Because a pentagon has 5 equal sides, we can use any of those sides in the formula.
Now, we know the pentagon has a side of 8in. So, we can substitute. We get
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Joe has a rectangular backyard. Its dimensions are 
by 
. If he wants to put up fencing around the perimeter, how much fencing will he need?
Joe has a rectangular backyard. Its dimensions are
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This problem is asking us to solve for how much fencing Joe requires to fence his backyard. In order to solve for this, we must find the perimeter of the backyard. The perimeter is a sum of the sides of a shape - or in this case, Joe's backyard. This makes sense to use, because fences usually line the outside - or the perimeter - of a backyard.
Perimeter is solved for through 
, where l is length and w is width. Although this problem does not explicitly state which value corresponds to width or length, it doesn't matter in this problem as both value will be multiplied by 
This problem is asking us to solve for how much fencing Joe requires to fence his backyard. In order to solve for this, we must find the perimeter of the backyard. The perimeter is a sum of the sides of a shape - or in this case, Joe's backyard. This makes sense to use, because fences usually line the outside - or the perimeter - of a backyard.
Perimeter is solved for through
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What is the perimeter of a square with a length of 
inches?
What is the perimeter of a square with a length of
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This problem asks for us to solve for the perimeter of a square that has a length of 
inches. The perimeter can be solved for using 
, where w means width and l means length.
In this kind of problem, it's important to remember that squares have 4 equal sides. This means that their lengths equal the width - therefore, it can be misleading to think there isn't enough information.
Therefore, the square has a perimeter of 
inches.
This problem asks for us to solve for the perimeter of a square that has a length of
In this kind of problem, it's important to remember that squares have 4 equal sides. This means that their lengths equal the width - therefore, it can be misleading to think there isn't enough information.
Therefore, the square has a perimeter of
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Jill would like to create a small pen for her fostered kittens. She plans on making an equilateral triangular shaped pen with only 
feet of fencing at her disposal. What is the greatest whole number side length the pen can have?
Jill would like to create a small pen for her fostered kittens. She plans on making an equilateral triangular shaped pen with only
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The problem states that Jill wants to make a pen in the shape of an equilateral triangle. This means the triangle will have three equal sides. With only 
feet of fencing, she wishes to make the largest triangle possible. In order to solve for the longest possible whole number length of the triangle pen, we must first utilize some concepts associated with perimeter.
Perimeter is the sum of all sides. This means that with 
feet of fencing, the sum of the three sides cannot exceed 
feet. Using this information, we can solve for the maximal side length:
if we set up an equation where all three sides are summed, we can set it equal to 
, keeping in mind that this is the limit. But we must also keep in mind that s cannot be a decimal number - it must be a whole number.
Because we are restrained by 
feet, we must round the value for s down. This would entail that the side of the pen can be 
feet maximum.
The problem states that Jill wants to make a pen in the shape of an equilateral triangle. This means the triangle will have three equal sides. With only
Perimeter is the sum of all sides. This means that with
if we set up an equation where all three sides are summed, we can set it equal to
Because we are restrained by
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