Perimeter and Sides - GED Math

Card 0 of 20

Question

The above figure is a regular octagon. Give its perimeter in yards.

Answer

A regular octagon has eight sides of equal length, so multiply the length of one side by eight:

$6 \frac{1}{4} \times 8 = \frac{25}{4} \times \frac{8}{1} = \frac{200}{4} = 50$ feet.

Divide by three to get the equivalent in yards:

$50 \div 3 = 16 \frac{2}{3}$ yards.

Compare your answer with the correct one above

Question

Identify the above polygon.

Answer

A polygon with eight sides is called an octagon.

Compare your answer with the correct one above

Question

Refer to the above figure.

Which of the following is not a valid alternative name for Polygon ?

Answer

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 ).

Compare your answer with the correct one above

Question

Refer to the above figure. All angles shown are right angles.

What is the perimeter of the figure?

Answer

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:

Compare your answer with the correct one above

Question

Refer to the above figure.

Which of the following segments is a diagonal of Pentagon ?

Answer

A diagonal of a polygon is a segment whose endpoints are nonconsecutive vertices of the polygon. Of the four choices, only $\overline{KM}$ fits this description.

Compare your answer with the correct one above

Question

Classify the above polygon.

Answer

A polygon with eight sides is called an octagon.

Compare your answer with the correct one above

Question

Hexagon is regular. If diagonals $\overline{EO}$ and $\overline{XG}$ are constructed, which of the following classifications applies to Quadrilateral ?

I) Rectangle

II) Rhombus

III) Square

IV) Trapezoid

Answer

The figure described is below.

Since the hexagon is regular, its sides are congruent, and its angles each have measure $180 ^{\circ } \times \frac{6-2}{6} = 180 ^{\circ } \times \frac{4}{6} = 120^{\circ }$ .

Also, each of the triangles are isosceles, and their acute angles measure $\frac{1}{2} (180^{\circ }- 120^{\circ }) = 30^{\circ }$ each. This means that each of the four angles of Quadrilateral measures $120 ^{\circ }- 30^{\circ }= 90^{\circ }$ , 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.

Compare your answer with the correct one above

Question

Classify the above polygon.

Answer

A polygon with six sides is called a hexagon.

Compare your answer with the correct one above

Question

What is the perimeter of a semicircle with an area of $16\pi$ ?

Answer

Write the formula for the area of a semicircle.

$A = \frac{1}{2}\pi r^2$

Substitute the area.

$16\pi = \frac{1}{2}\pi r^2$

Multiply by 2, and divide by pi on both sides.

$\frac{16\pi \cdot (2)}{\pi}=\frac{ \frac{1}{2}\cdot (2)\pi r^2}{\pi}$

The equation becomes:

Square root both sides and factor the right side.

$\sqrt{r^2} =\sqrt{32}$

$r=4\sqrt{2}$

The diameter is double the radius.

$D=8\sqrt{2}$

The circumference is half the circumference of a full circle.

$C_{semi}=\frac{1}{2}\pi D = 4\pi \sqrt{2}$

The perimeter is the sum of the diameter and the half circumference.

The answer is: $8\sqrt2+ 4\pi \sqrt2$

Compare your answer with the correct one above

Question

A hexagon has a perimeter of 90in. Find the length of one side.

Answer

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

$90\text{in} = 6a$

$\frac{90\text{in}}{6} = \frac{6a}{6}$

$15\text{in} = a$

$a = 15\text{in}$

Therefore, the length of one side of the hexagon is 15in.

Compare your answer with the correct one above

Question

A hexagon has a perimeter of 138cm. Find the length of one side.

Answer

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

$138\text{cm} = 6a$

$\frac{138\text{cm}}{6} = \frac{6a}{6}$

$23\text{cm} = a$

$a = 23\text{cm}$

Therefore, the length of one side of the hexagon is 23cm.

Compare your answer with the correct one above

Question

A hexagon has a perimeter of 126in. Find the length of one side.

Answer

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

$126\text{in} = 6a$

$\frac{126\text{in}}{6} = \frac{6a}{6}$

$21\text{in} = a$

$a = 21\text{in}$

Therefore, the length of one side of the hexagon is 21in.

Compare your answer with the correct one above

Question

A hexagon has a perimeter of 198cm. Find the length of one side.

Answer

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

$198\text{cm} = 6a$

$\frac{198\text{cm}}{6} = \frac{6a}{6}$

$33\text{cm} = a$

$a = 33\text{cm}$

Therefore, the length of one side of the hexagon is 33cm.

Compare your answer with the correct one above

Question

Figure NOT drawn to scale.

Refer to the above figure. Every angle shown is a right angle.

Give its perimeter.

Answer

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 :

Compare your answer with the correct one above

Question

What is the perimeter of a semicircle with a radius of 4?

Answer

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.

$C_{semi} = \frac{1}{2}(2\pi r) = \pi r = 4\pi$

The diameter is double the radius, or .

Sum the circumference and the diameter to get the perimeter.

The answer is: $4\pi +8$

Compare your answer with the correct one above

Question

Find the perimeter of a hexagon with a side of length 9cm.

Answer

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

$P = 6(9\text{cm})$

$P = 54\text{cm}$

Compare your answer with the correct one above

Question

Find the perimeter of a pentagon with a side of length 8in.

Answer

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

$P = 5(8\text{in})$

$P = 40\text{in}$

Compare your answer with the correct one above

Question

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?

Answer

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

Compare your answer with the correct one above

Question

What is the perimeter of a square with a length of inches?

Answer

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.

Compare your answer with the correct one above

Question

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?

Answer

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.

$\frac{3s}{3}=\frac{16}{3}$

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.

Compare your answer with the correct one above

Tap the card to reveal the answer