Geometry and Graphs

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GED Math › Geometry and Graphs

Questions 1 - 10

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

$33\text{cm}$

$32\text{cm}$

$29\text{cm}$

$31\text{cm}$

$28\text{cm}$

Explanation

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.

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

$21\text{in}$

$20\text{in}$

$18\text{in}$

$22\text{in}$

$9\text{in}$

Explanation

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.

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

$23\text{cm}$

$22\text{cm}$

$19\text{cm}$

$21\text{cm}$

$18\text{cm}$

Explanation

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.

Find the measure of angle B if it is the supplement to angle A:

$m\angle A=115^{o}$

$m\angle B=65^{o}$

$m\angle B=21^{o}$

$m\angle B=205^{o}$

$m\angle B=5^{o}$

Explanation

If two angles are supplementary, that means the sum of their degrees of measure will add up to 180. In order to find the measure of angle B, subtract angle A from 180 like shown:

$m\angle B=180^{o}-115^{o}=65^{o}$

This gives us a final answer of 65 degrees for angle B.

In the figure above, $a\parallel b$ . If the measure of $\measuredangle 1=6x^{\circ}$ and $\measuredangle 6=4x^{\circ}$ , what is the measure of $\measuredangle8$ ?

$108^{\circ}$

$122^{\circ}$

$72^{\circ}$

$58^{\circ}$

Explanation

Since we have two parallel lines, we know that $\measuredangle1=\measuredangle4$ since they are opposite angle.

We also know that $\measuredangle 4 \text{ and }\measuredangle 6$ are supplementary because they are consecutive interior angles. Thus, we know that $\measuredangle 1$ is also supplementary to $\measuredangle6$ .

We can then set up the following equation to solve for .

Thus, $\measuredangle 1=108^{\circ}$ and $\measuredangle6=72^{\circ}$ .

Now, notice that $\measuredangle 8=\measuredangle 4$ because they are corresponding angles. Thus, $\measuredangle 8=\measuredangle 1=108^{\circ}$ .

A square and a circle share a center as shown by the figure below.

If the length of a side of the square is and is half the length of the radius of the circle, to the nearest hundredths place, find the area of the shaded region.

Explanation

In order to find the area of the shaded region, we will need to find the area of the circle then subtract the area of the square from it.

Start by finding the area of the square. Since we know the side length of the square, we can write the following:

$\text{Area of Square}=4^2=16$

Next, we find the area of the circle. Since the question states that the length of a side of the square is half the radius of the circle, the radius of the circle must be . Thus, we can find the area of the circle.

$\text{Area of Circle}=\pi r^2=\pi(8)^2=64\pi$

Now, subtract these two values to find the area of the shaded region.

$\text{Area of Shaded Region}=64\pi-16=185.06$

Find the area of a square with a side of .

Explanation

Write the formula for the area of a square.

Substitute the side.

The answer is:

A rectangle has length 10 inches and width 5 inches. Each dimension is increased by 3 inches. By what percent has the area of the rectangle increased?

Explanation

The area of a rectangle is its length times its width.

Its original area is $10 \times 5 = 50$ square inches; its new area is $13 \times 8 = 104$ square inches. The area has increased by

$\frac{104 - 50}{50 } \times 100 = \frac{54}{50 } \times 100 = 108 %$ .

If the area of square is $\text{in}^2$ , what is its perimeter?

$52;\textup{in}$

$13;\textup{in}$

$26;\textup{in}$

$40;\textup{in}$

$22;\textup{in}$

Explanation

Figuring out the perimeter of a square from this information is luckily pretty easy. Since the sides of a square are all the same size, you know also that .