GED Math - Geometry and Graphs

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.

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:

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.

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

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

Determine the area of a circle in square feet with a radius of 12 inches.

$\pi$

$24\pi$

$2\pi$

$12\pi$

$144\pi$

Explanation

Write the formula for the area of a circle.

$A=\pi r^2$

Convert the radius to feet. There are 12 inches in a foot.

This means the radius in feet is 1.

Substitute the radius in feet to obtain the area in feet squared.

$A=\pi (1\textup{ ft})^2 = \pi \textup{ ft}^2$

The answer is: $\pi$

Determine the circumference of a circle with a radius of $\frac{\pi}{4}$ .

$\frac{\pi ^2}{2}$

$\frac{\pi }{2}$

$\frac{\pi}{8}$

$\frac{\pi^2}{8}$

$\frac{1}{2}$

Explanation

Write the formula for the circumference of a circle.

$C=\2\pi r$

Substitute the radius.

$C=\2\pi (\frac{\pi}{4}) = \frac{\pi ^2}{2}$

The answer is: $\frac{\pi ^2}{2}$

The image is not to scale.

If the sum of two angles results in a complementary angle, what is the measure of the unknown angle?

Capture2

$60^{\circ}$

$150^{\circ}$

$30^{\circ}$

$90^{\circ}$

$20^{\circ}$

Explanation

With the provided image, we are asked to solve for the measure of the unknown angle.

Capture2

First, we must understand some information before attempting to solve the problem. The problem provides the information that the two angles summed up result in a complimentary angle. This is another way to say that when we add the measures of the two angles, it will equal $90^{\circ}$ .

This becomes a problem where we solve for a missing variable now. We can call the unknown angle x. We would set this up in equation format accordingly:

Now, we can solve for x.

$x+30{\color{Red} -30}=90{\color{Red} -30}$

$x=60^{\circ}$

Therefore, the unknown angle is $60^{\circ}$ .

Let $\pi = 3.14$

Find the area of a circle with a diameter of 8in.

$50.24\text{in}^2$

$200.96\text{in}^2$

$25.12\text{in}^2$

$153.86\text{in}^2$

$100.48\text{in}^2$

Explanation

To find the area of a circle, we will use the following formula:

$A = \pi \cdot r^2$

where r is the radius of the circle.

Now, we know $\pi = 3.14$ . We know the diameter of the circle is 8in. We know the diameter is two times the radius. Therefore, the radius is 4in. So, we substitute. We get

$A = 3.14 \cdot(4\text{in})^2$

$A = 3.14 \cdot 16\text{in}^2$

$A = 50.24\text{in}^2$

Which of the following can be the measures of the three angles of an acute isosceles triangle?

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$

$32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$

$45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$

$50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$

$80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$

Explanation

For the triangle to be acute, all three angles must measure less than $90 ^{\circ }$ . We can eliminate $32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$ and $45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$ for this reason.

In an isosceles triangle, at least two angles are congruent, so we can eliminate $50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$ .

The degree measures of the three angles of a triangle must total 180, so, since $80 ^{\circ }+ 80 ^{\circ }+ 40 ^{\circ } = 200^{\circ }$ , we can eliminate $80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$ .

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$ is correct.

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 $\measuredangle6$ .