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HSPT Math : Geometry

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Example Questions

Example Question #12 : Rectangles

A rectangular prism has length 24 inches, width 18 inches, and height 15 inches. Give its surface area in square feet.

Possible Answers:

$16 \textrm{ ft}^{2}$

$32 \textrm{ ft}^{2}$

$13\frac{1}{4} \textrm{ ft}^{2}$

$15\frac{3}{4} \textrm{ ft}^{2}$

$14\frac{3}{4} \textrm{ ft}^{2}$

Correct answer:

$14\frac{3}{4} \textrm{ ft}^{2}$

Explanation:

Divide each dimension in inches by 12 to convert from inches to feet:

$L = 24 \div 12 = 2$ feet

$W = 18 \div 12 = 1 \frac{1}{2} = \frac{3}{2}$ feet

$H = 15 \div 12 = 1 \frac{1}{4} = \frac{5}{4}$ feet

Now, substitute in the surface area formula:

A = 2LW + 2WH + 2LH

$A = 2\cdot 2 \cdot \frac{3}{2} + 2 \cdot \frac{3}{2}\cdot \frac{5}{4} + 2\cdot 2 \cdot \frac{5}{4}$

$A =6 + \frac{15}{4} + 5$

$A =6 + 3 \frac{3}{4} + 5$

$A =14\frac{3}{4}ft^{2}$

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Example Question #21 : Geometry

The area of a rectangle with a length of and a width of is $84\ in^2$ . Find .

Possible Answers:

1.21

1.51

1.11

1.41

1.31

Correct answer:

1.41

Explanation:

The area of a rectangle is the product of length and width:

$7x\times 6x=84\Rightarrow 42x^2=84\Rightarrow x^2=2\Rightarrow x=\sqrt{2}\approx 1.41$

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Example Question #71 : Quadrilaterals

Give the area of a rectangle with a length of 3.8 ft and a width of $2.4\ ft$ .

Possible Answers:

$1313.28\ in^2$

$131.28\ in^2$

$1413.28\ in^2$

$130\ in^2$

$1300\ in^2$

Correct answer:

$1313.28\ in^2$

Explanation:

We know that:

$Area=a\times b$

where:

$a=Length \ of\ the\ rectangle$

$b= Width\ of\ the\ rectangle$

So we can write:

$Area=3.8\ ft \times 2.4\ ft=(3.8\times 12\ in)\times (2.4\times 12\ in)=1313.28\ in^2$

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Example Question #23 : Geometry

A rectangular table has a length of $2.2\ m$ and a width of $1.5\ m$ . Give the area of the table.

Possible Answers:

$33000\ cm^2$

$330\ cm^2$

$30000\ cm^2$

$3000\ cm^2$

$3300\ cm^2$

Correct answer:

$33000\ cm^2$

Explanation:

We know that:

$Area=a\times b$

where:

$a=Length \ of\ the\ rectangle$

$b= Width\ of\ the\ rectangle$

So we can write:

$Area=2.2\ m \times 1.5\ m=(2.2\times 100\ cm)\times (1.5\times 100\ cm)=33000\ cm^2$

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Example Question #104 : Plane Geometry

The length of a rectangle is three times longer than its width. If the width of the rectangle is meters, give the area of the rectangle.

Possible Answers:

$30\ m^2$

$24\ m^2$

$27\ m^2$

$33\ m^2$

$21\ m^2$

Correct answer:

$27\ m^2$

Explanation:

The length of the rectangle would be: $3\times 3=9\ m$

We know that:

$Area=a\times b$

where:

$a=Length \ of\ the\ rectangle$

$b= Width\ of\ the\ rectangle$

So we can write:

$Area=9\times 3=27\ m^2$

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Example Question #173 : Plane Geometry

Which of the following is the area of a rectangle with a width of 4 feet and a length that is twice the width?

Possible Answers:

$34\ \text{ft}^2$

$32\ \text{ft}^2$

$64\ \text{ft}^2$

$36\ \text{ft}^2$

$16\ \text{ft}^2$

Correct answer:

$32\ \text{ft}^2$

Explanation:

The area of a rectangle is found by multiplying the width by the length.

$A=w\times l$

We know that the width is 4 feet and the the length must be twice the width. Multiply the width by 2 to find the length.

$l=2\times w$

$l=2\times4=8$

Multiply the length and width to find the area.

$4\times8=32$

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Example Question #331 : Ssat Middle Level Quantitative (Math)

Jeff decided to build a play area for his guinea pigs. The play area would be an enclosure 6 feet long, 2 feet wide, and 2 feet tall. In cubic feet, how big is the play area?

Possible Answers:

$24\ ft^{3}$

$12\ ft^{3}$

$16\ ft^{3}$

$18\ ft^{3}$

Correct answer:

$24\ ft^{3}$

Explanation:

The cubic feet of an area is found by multiping the length times the width times the height. Given that the length is six feet, the width is two feet, and that the height is two feet, the total cubic area would be found using this equation:

$length\cdot width \cdot heighth$

Here is the equation with the appropriate numbers plugged in:

$6\cdot 2\cdot 2 = 24$

Therefore, 24 cubic feet is the correct answer.

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Example Question #1 : Geometry

Jessica's blanket is 12 square feet. Lisa has a blanket that is half the size of Jessica's blanket. Which of the following are possible dimensions of Lisa's blanket?

Possible Answers:

$3\ ft\times2\ ft$

$1\ ft\times12\ ft$

$3\ ft\times3\ ft$

$2\ ft\times2\ ft$

Correct answer:

$3\ ft\times2\ ft$

Explanation:

The area of a rectangle if found by multiplying the length times the width. Here, we know that Lisa's blanket is half the area of Jessica's blanket. Since Jessica's blanket is 12 square feet, that means that Lisa's blanket must be 6 square feet.

The only length and width values that give us 6 square feet when multiplied by one another are 3 feet by 2 feet. This is therefore the correct answer.

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Example Question #1 : How To Find The Area Of A Square

Which of the following is equal to the area of a square with perimeter 8 meters?

Possible Answers:

$160,000 \textrm{ cm}^{2}$

$20,000 \textrm{ cm}^{2}$

$40,000 \textrm{ cm}^{2}$

$80,000 \textrm{ cm}^{2}$

Correct answer:

$40,000 \textrm{ cm}^{2}$

Explanation:

The sidelength of a square is one-fourth its perimeter, so the sidelength here is one-fourth of 8, or 2, meters. One meter is equal to 100 centimeters, so the sidelength is 200 centimeters. Square this to get the area:

$200 ^{2} = 200 \times 200 = 40,000$ square centimeters.

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Example Question #2 : How To Find The Area Of A Square

Which of the following is the area of a square with perimeter 7 feet?

Possible Answers:

$529 \textrm{ in}^{2}$

$441 \textrm{ in}^{2}$

$729 \textrm{ in}^{2}$

$961 \textrm{ in}^{2}$

Correct answer:

$441 \textrm{ in}^{2}$

Explanation:

Convert 7 feet to inches by multiplying by 12: $7 \times 12 = 84$ inches.

The sidelength of a square is one-fourth its perimeter, so the sidelength here is one-fourth of 84 inches. This is $84 \div 4 = 21$ inches.

Square this to get the area:

$21 ^{2} = 21 \times 21 = 441$ square inches

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HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #12 : Rectangles

Example Question #21 : Geometry

Example Question #71 : Quadrilaterals

Example Question #23 : Geometry

Example Question #104 : Plane Geometry

Example Question #173 : Plane Geometry

Example Question #331 : Ssat Middle Level Quantitative (Math)

Example Question #1 : Geometry

Example Question #1 : How To Find The Area Of A Square

Example Question #2 : How To Find The Area Of A Square

All HSPT Math Resources

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