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HSPT Math : Concepts

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Example Questions

Example Question #1 : Rectangles

Which of the following is equal to the area of a rectangle with length 250 centimeters and width 140 centimeters?

Possible Answers:

$350 \textrm{ m}^{2}$

$3.5 \textrm{ m}^{2}$

$0.35 \textrm{ m}^{2}$

$35 \textrm{ m}^{2}$

Correct answer:

$3.5 \textrm{ m}^{2}$

Explanation:

Divide each dimension by 100 to convert centimeters to meters:

$250 \div 100 = 2.5$

$140 \div 100 = 1.4$

Multiply length by width:

$2.5 \times 1.4 = 3.5$ square meters

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Example Question #3 : Rectangles

A hectare is a unit of area equal to 10,000 square meters.

A rectangular plot of land measures 1,400 meters by 800 meters. Give the area of this plot in hectares.

Possible Answers:

$920 \textrm{ hectares}$

$112 \textrm{ hectares}$

$92 \textrm{ hectares}$

$1,120 \textrm{ hectares}$

Correct answer:

$112 \textrm{ hectares}$

Explanation:

Multiply length times width to get the area in square meters:

$A = 1,400 \times 800 = 1,120,000$ square meters

Divide by 10,000 to convert to hectares:

$1,120,000 \div 10,000 = 112$ hectares

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Example Question #5 : Rectangles

Which of the following is equal to the area of a rectangle with length 27 inches and width 15 inches?

Possible Answers:

$3.1875 \textrm{ ft}^{2}$

$2.8125 \textrm{ ft}^{2}$

$2.9375 \textrm{ ft}^{2}$

$3.0625 \textrm{ ft}^{2}$

Correct answer:

$2.8125 \textrm{ ft}^{2}$

Explanation:

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

$27 \div 12 = 2.25$

$15 \div 12 = 1.25$

Multiply length by width:

$2.25 \times 1.25 = 2.8125$ square feet

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Example Question #163 : Plane Geometry

Which of the following is equal to the area of a rectangle with length feet and width $1 \frac{1}{2}$ feet?

Possible Answers:

$576 \textrm{ in}^{2}$

$648 \textrm{ in}^{2}$

$324\textrm{ in}^{2}$

$432 \textrm{ in}^{2}$

Correct answer:

$648 \textrm{ in}^{2}$

Explanation:

Multiply each dimension by 12 to convert from feet to inches:

$3 \times 12 = 36 \textrm{ in}$

$1 \frac{1}{2} \times 12 = 18 \textrm{ in}$

Now multiply this length and width to get the area:

$36 \times 18 = 648 \textrm{ in}^{2}$

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Example Question #171 : Plane Geometry

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

Possible Answers:

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

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

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

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

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

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 #62 : Quadrilaterals

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

Possible Answers:

1.51

1.11

1.41

1.31

1.21

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 #11 : How To Find The Area Of A Rectangle

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

Possible Answers:

$131.28\ in^2$

$130\ in^2$

$1300\ in^2$

$1313.28\ in^2$

$1413.28\ in^2$

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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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1 : Rectangles

Example Question #3 : Rectangles

Example Question #5 : Rectangles

Example Question #163 : Plane Geometry

Example Question #171 : Plane Geometry

Example Question #62 : Quadrilaterals

Example Question #11 : How To Find The Area Of A Rectangle

Example Question #23 : Geometry

Example Question #104 : Plane Geometry

Example Question #173 : Plane Geometry

All HSPT Math Resources

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