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Pre-Algebra : Geometry

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Example Questions

Example Question #21 : Geometry

A square has a base length of 100 . What is the area?

Possible Answers:

100

5000

10000

1000

Correct answer:

10000

Explanation:

Write the formula to find the area of a square given its side length.

A=s^2

A=100^2 = 10000

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Example Question #22 : Area Of A Rectangle Or Square

Find the area of a square if the perimeter is $4\pi$ .

Possible Answers:

$\pi$

$\pi^2$

$\frac{4}{\pi}$

Correct answer:

$\pi^2$

Explanation:

Write the formula for the area of a square.

A=s^2

In order to find the area of the square, we need to find the length of the side given the perimeter. There are four equal sides in a square. Divide the perimeter by 4.

$s=\frac{P}{4} = \frac{4\pi}{4} = \pi$

Substitute the side in the area formula.

$A=\pi^2$

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Example Question #23 : Area Of A Rectangle Or Square

Determine the area of a rectangle with a length and width of 10x .

Possible Answers:

2x+100

20x^2

100x^2

1000x^2

40x^2

Correct answer:

100x^2

Explanation:

Write the formula for the area of a rectangle.

$A= \textup{Length } \times \textup{Width}$

Substitute the given length and width into this equation.

$A= (10x)(10x) = 10\cdot x \cdot 10\cdot x = 100x^2$

The area of the rectangle is: 100x^2

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Example Question #22 : Geometry

Find the area of a rectangle if the base length is and the height is 9x+3 .

Possible Answers:

12x+3

27x^2+9x

12x^2+9

12x+6

18x^2

Correct answer:

27x^2+9x

Explanation:

Write the formula for the area of a rectangle.

A=bh

Substitute the dimension.

A=(3x)(9x+3)

Use the distributive property to expand the area.

A = (3x)(9x)+ (3x)(3)

Multiply the terms.

A = 27x^2+ 9x

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Example Question #25 : Area Of A Rectangle Or Square

Find the area of a square if ths side of the square is x^5 .

Possible Answers:

$2x^{10}$

$x^{10}$

2x^5

$x^{25}$

$x^{20}$

Correct answer:

$x^{10}$

Explanation:

Write the formula for the area of the square.

$A_\textup{square}=s^2$

Substitute the side length into the formula.

$A_\textup{square}=s^2 = (x^5)^2$

Expand the terms. We can either use the product rule or power rule for exponents to solve this.

$(x^5)^2 = (x^5)(x^5)=x^{10}$

The area is: $x^{10}$

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Example Question #26 : Area Of A Rectangle Or Square

If the square has a length of 5 kilometers, what is the area of the square in meters?

Possible Answers:

$250 \textup{ meters}^2$

$25,000 \textup{ meters}^2$

$25,000,000 \textup{ meters}^2$

$250,000 \textup{ meters}^2$

$2,500 \textup{ meters}^2$

Correct answer:

$25,000,000 \textup{ meters}^2$

Explanation:

Write the formula for the area of a square.

A=s^2

Convert 5 kilometers to meters.

There are 1000 meters in a kilometer.

$5 \textup{ km} (\frac{1000 \textup{ meters}}{1 \textup{ km}}) = 5000 \textup{ meters}$

Substitute this value into the area formula.

$A=(5000 \textup{ meters})^2 = 25,000,000 \textup{ meters}^2$

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Example Question #23 : Geometry

Find the area of a square with a diagonal of $10\sqrt{2}$ .

Possible Answers:

200

400

100

Correct answer:

100

Explanation:

In order to find the length of the side of the square, we need to use the following formula:

$s= \frac{d}{\sqrt2}$

Substitute the diagonal into the formula to find the side.

$s= \frac{10\sqrt{2}}{\sqrt2} = 10$

Now that the side is known, write the formula for the area of the square.

A=s^2

Substitute the side length and expand.

A=10^2 = (10)(10) = 100

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Example Question #28 : Area Of A Rectangle Or Square

Mr. and Mrs. Johnson have a yard that looks like the following.

Area2

The length of the yard is 36 ft, and the width is a third of the length . If either of them have to mow their yard, what is the total area they will mow?

Possible Answers:

$\small 432\text{ft}^2$

$\small 96\text{ft}$

$\small 432\text{ft}$

$\small 96\text{ft}^2$

$48 \text{ft}^2$

Correct answer:

$\small 432\text{ft}^2$

Explanation:

The width of the yard is a third of the length. If the length is 36ft, we must find what a third of 36 equals. To do that, we simply divide by 3.

$\small \frac{36}{3} = 12$

So the width of the yard is 12ft.

The formula to find the area of a rectangle is

$\text{area} = length * width$

$= 36 \text{ft} * 12 \text{ft}$

$= 432 \text{ft}^2$

So the total area Mr. or Mrs. Johnson will have to mow is $432 \text{ft}^2$

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Example Question #23 : Geometry

David wants to make a flower bed that is 10 feet long and 5 feet wide. He also wants to put a 2 foot-wide concrete path around it. How many square feet is the path?

Possible Answers:

92ft^2

60ft^2

76ft^2

100ft^2

52ft^2

Correct answer:

76ft^2

Explanation:

A length of 10ft and path width of 2ft means each length has 20 square feet. The width of 5ft and path width of 2ft means each width is 10 square feet. Each corner also has a 4 square foot section, which means an extra 16 square feet. Add them together:

20 + 20 + 10 + 10 + 16 = 76ft^2

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Example Question #30 : Area Of A Rectangle Or Square

What is the area of a square with a side length of inches?

Possible Answers:

in^2

Correct answer:

in^2

Explanation:

To find the area of a square, simply multiply the side length by itself. Because the side length of the square in question is , the best answer is:

$7\times 7=49$

in^2

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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #21 : Geometry

Example Question #22 : Area Of A Rectangle Or Square

Example Question #23 : Area Of A Rectangle Or Square

Example Question #22 : Geometry

Example Question #25 : Area Of A Rectangle Or Square

Example Question #26 : Area Of A Rectangle Or Square

Example Question #23 : Geometry

Example Question #28 : Area Of A Rectangle Or Square

Example Question #23 : Geometry

Example Question #30 : Area Of A Rectangle Or Square

All Pre-Algebra Resources

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