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Pre-Algebra : Geometry

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Example Questions

Example Question #11 : Geometry

A cube has a sidelength that measures 16 inches. What is the total area of two of its sides or faces?

Possible Answers:

430in^2

256in^2

None of the other answers.

512in^2

526in^2

Correct answer:

512in^2

Explanation:

All faces of a cube have equal measurements and are squares. So if a cube has a sidelength that measures 16 inches, you know that all its sides measure 16 inches.

The surface area of one face of the cube is: A=s*s=16*16=256in^2

Since the question asks for the surface area of two faces of the cube we double the area found for one side: 512in^2

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Example Question #12 : Geometry

A squre has perimeter 16.

What is its area?

Possible Answers:

Correct answer:

Explanation:

Because a square has four equal sides, you can divide the perimeter by four to discover each side length is 4. The equation for area of a square is A=b*h ,

so 4*4=16

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Example Question #13 : Geometry

What is the area of a rectangle with a length of 2 and a width of 100?

Possible Answers:

208

102

104

108

200

Correct answer:

200

Explanation:

Write the formula for the area of a rectangle.

$A=L\times W$

Substitute the dimensions and solve for the area.

$A=2\times 100 = 200$

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Example Question #14 : Geometry

Jack is painting one side of his house. It is 20 meters long and 15 meters high. A can of paint covers 40 meters squared. How many cans will he need to buy to cover the wall?

Possible Answers:

7.5 Cans

7 Cans

8 Cans

9 Cans

8.5 Cans

Correct answer:

8 Cans

Explanation:

The total area of the wall is 20 * 15 = 300 meters squared.

Each can covers 40 meters squared. Therefore, to find the number of cans needed we will need to divide the total area by the amount of area each can covers.

$\frac{300}{ 40} = 7.5$

However, you cannot buy 7.5 cans so the correct answer is 8 Cans.

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Example Question #15 : Geometry

Find the area of a square if the side is 25.

Possible Answers:

125

625

100

Correct answer:

625

Explanation:

Write the formula for the area of a square.

A=s^2

Plug in the side.

A=(25)^2 = 625

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Example Question #16 : Area

Find the area of a square with a diagonal of $3\sqrt2$ .

Possible Answers:

$9\sqrt2$

$3\sqrt2$

Correct answer:

Explanation:

Write the formula to find the side length given the length of the diagonal.

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

Substitute the diagonal to find the side.

$s= \frac{3\sqrt2}{\sqrt2} = 3$

Write the formula for area of the square and substitute the side.

A=s^2 = 3^2 =9

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Example Question #16 : Geometry

Find the area of a rectangle if the perimeter is 10.

Possible Answers:

$\textup{There is not enough information.}$

Correct answer:

$\textup{There is not enough information.}$

Explanation:

Write the formula for the perimeter of a rectangle.

P=2W+2L

Possible combinations of width and length for the perimeter are:

First possibility: W=1,L=4

Second possibility: W=2, L=3

These are only 2 combinations of many possible dimensions.

Write the area of a rectangle.

A=LW

The area for the first possibility is 4, and the area for the second possibility is 6. Each combination of length and width will yield a different area. Without a known dimension for length and width of the rectangle, we cannot solve for a known area.

The correct answer is: $\textup{There is not enough information.}$

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Example Question #17 : Geometry

What is the area of a square if the side of the square is $\pi$ ?

Possible Answers:

$\pi ^2$

$4\pi$

$2\pi$

6.28

$\pi ^3$

Correct answer:

$\pi ^2$

Explanation:

Write the formula for the area of a square and substitute the side.

$A=s^2 = \pi ^2$

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Example Question #19 : Area

Find the area of a rectangle if the perimeter is 10, and the width is 4.

Possible Answers:

Correct answer:

Explanation:

Write the perimeter formula for rectangles.

P=2(W+L)

Substitute the perimeter and the width to find the length. The length will be needed to find the area.

10=2(4+L)

Solve for .

5=(4+L)

L=1

Write the formula for the area of a rectangle and solve for the area.

A=LW = (1)(4)=4

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Example Question #20 : Area

Find the area of a rectangle if the length is $\frac{2}{3}$ and the base is $\frac{5}{9}$ .

Possible Answers:

$\frac{32}{37}$

$\frac{1}{2}$

$\frac{10}{27}$

$\frac{7}{12}$

$\frac{7}{27}$

Correct answer:

$\frac{10}{27}$

Explanation:

Write the formula for the area of a rectangle.

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

Substitute the dimensions.

Remember when multiplying fractions, multiply the numerators together and multiply the denominators together.

$A= \frac{2}{3} \times \frac{5}{9} = \frac{10}{27}$

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Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #11 : Geometry

Example Question #12 : Geometry

Example Question #13 : Geometry

Example Question #14 : Geometry

Example Question #15 : Geometry

Example Question #16 : Area

Example Question #16 : Geometry

Example Question #17 : Geometry

Example Question #19 : Area

Example Question #20 : Area

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