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TACHS Math : Area

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Example Questions

Example Question #1 : Area

A square has perimeter 24 feet. Give its area.

Possible Answers:

18 square feet

36 square feet

576 square feet

144 square feet

Correct answer:

36 square feet

Explanation:

The perimeter of a figure is the sum of the lengths of its sides. A square comprises four sides of equal length, so, if the perimeter of the square is 24 feet, then each side has length

$24 \div 4 = 6$ $\displaystyle 24 \div 4 = 6$ feet.

The area of the square is equal to the length of a side multiplied by itself, so the area of this square is

$6\times6= 36$ $\displaystyle 6\times6= 36$ square feet.

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Example Question #3 : Geometry

Jennifer wants to wallpaper her room which is made up for four rectangular walls each measuring at $\displaystyle 15$ feet by $\displaystyle 12$ feet. If each roll of wallpaper covers $\displaystyle 60$ square feet of space, how many rolls of wallpaper will Jennifer need?

Possible Answers:

$\displaystyle 13$

$\displaystyle 12$

$\displaystyle 11$

$\displaystyle 10$

Correct answer:

$\displaystyle 12$

Explanation:

Start by finding out the total square footage of wallpaper needed.

Find the area of one wall. Recall that in order to find the area of a rectangle, you must multiply the length by the width.

$\text{Area of One Wall}=15 \times 12=180$ $\displaystyle \text{Area of One Wall}=15 \times 12=180$

Since we have four identical walls,

$\text{Total Area of Walls}=4 \times 180 =720$ $\displaystyle \text{Total Area of Walls}=4 \times 180 =720$

Now divide this by the amount of square feet covered by each roll of wallpaper to find how many rolls are needed.

$\text{Rolls of wallpaper needed}=\frac{720}{60}=12$ $\displaystyle \text{Rolls of wallpaper needed}=\frac{720}{60}=12$

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Example Question #4 : Geometry

Find the area of a circle with the following radius:

r=7 $\displaystyle r=7$

Possible Answers:

$48\pi$ $\displaystyle 48\pi$

$7\pi$ $\displaystyle 7\pi$

$49\pi$ $\displaystyle 49\pi$

$14\pi$ $\displaystyle 14\pi$

$16\pi$ $\displaystyle 16\pi$

Correct answer:

$49\pi$ $\displaystyle 49\pi$

Explanation:

The area of a circle can be calculated using the following formula:

$A=\pi r^2$ $\displaystyle A=\pi r^2$

In this formula the radius is denoted by the variable, $\displaystyle r$.

Substitute in the known variables and solve for the circle's area.

$A=\pi \times 7^2$ $\displaystyle A=\pi \times 7^2$

$A=49\pi$ $\displaystyle A=49\pi$

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Example Question #5 : Geometry

Which is equal to the radius of a circle with area $400 \pi$ $\displaystyle 400 \pi$

Possible Answers:

$\displaystyle 40$

100 $\displaystyle 100$

200 $\displaystyle 200$

$\displaystyle 20$

Correct answer:

$\displaystyle 20$

Explanation:

The formula for the area $\displaystyle A$ of a circle, given its radius $\displaystyle r$, is $A = \pi r^{2}$ $\displaystyle A = \pi r^{2}$. Replace $\displaystyle A$ with $400 \pi$ $\displaystyle 400 \pi$:

$\pi r^{2} = 400 \pi$ $\displaystyle \pi r^{2} = 400 \pi$

To find the radius $\displaystyle r$, first, divide both sides by $\pi$ $\displaystyle \pi$:

$\frac{\pi r^{2}}{\pi} = \frac{400 \pi}{\pi}$ $\displaystyle \frac{\pi r^{2}}{\pi} = \frac{400 \pi}{\pi}$

$r^{2} = 400$ $\displaystyle r^{2} = 400$

Now, find the square root of both sides. Since $400 = 20 \times 20$ $\displaystyle 400 = 20 \times 20$, 20 is the square root of 400, so

r = 20 $\displaystyle r = 20$.

The radius of the given circle is 20.

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Example Question #6 : Geometry

To determine whether a machine on an assembly line is filling bottles with the correct amount of soda, twenty bottles are selected. The tenth bottle and every tenth bottle after that are taken off the line and examined.

This is an example of which kind of sampling?

Possible Answers:

Systematic sampling

Convenience sampling

Cluster sampling

Stratified sampling

Correct answer:

Systematic sampling

Explanation:

The sample in this scenario is selected from the population by choosing obects that occur at regular intervals. That makes this an example of systematic sampling.

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Example Question #31 : Math

What is the area of a circle that has a diameter of $\displaystyle 12$?

Possible Answers:

113.1 $\displaystyle 113.1$

452.4 $\displaystyle 452.4$

37.7 $\displaystyle 37.7$

92.6 $\displaystyle 92.6$

Correct answer:

113.1 $\displaystyle 113.1$

Explanation:

Recall how to find the area of a circle:

$\text{Area of Circle}=\pi \times \text{radius}^2$ $\displaystyle \text{Area of Circle}=\pi \times \text{radius}^2$

To find the length of the radius, divide the diameter by two.

$\text{radius}=\frac{12}{2}=6$ $\displaystyle \text{radius}=\frac{12}{2}=6$

Now, plug it into the equation for the area of a circle.

$\text{Area of Circle}=\pi \times 6^2=36\pi=113.1$ $\displaystyle \text{Area of Circle}=\pi \times 6^2=36\pi=113.1$

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TACHS Math : Area

Study concepts, example questions & explanations for TACHS Math

All TACHS Math Resources

Example Questions

Example Question #1 : Area

Example Question #3 : Geometry

Example Question #4 : Geometry

Example Question #5 : Geometry

Example Question #6 : Geometry

Example Question #31 : Math

All TACHS Math Resources

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