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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Plane Geometry

The hypotenuse of a right triangle is 25 inches; it has one leg 15 inches long. Give its area in square feet.

Possible Answers:

$1 \frac{1}{24} \textrm{ ft}^{2}$

$1 \frac{1}{12} \textrm{ ft}^{2}$

$2 \frac{5}{48} \textrm{ ft}^{2}$

$1 \frac{13}{24}\textrm{ ft} ^{2}$

$2 \frac{29}{48} \textrm{ ft}^{2}$

Correct answer:

$1 \frac{1}{24} \textrm{ ft}^{2}$

Explanation:

The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set c = 25, b = 15 :

$a^{2} = c^{2} - b^{2}$

$a^{2} = 25^{2} - 15^{2}$

$a^{2} = 625-225$

$a^{2} =400$

$a = \sqrt{400} = 20$

The legs are 15 and 20 inches long. Divide both dimensions by 12 to convert from inches to feet:

$20 \div 12 = \frac{5}{3}$ feet

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

Now find half their product:

$A = \frac{1}{2} \times \frac{5}{3}\times \frac{5}{4} = \frac{25}{24} = 1 \frac{1}{24}$ square feet

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Example Question #281 : Ssat Middle Level Quantitative (Math)

What is the area of a square with perimeter 64 inches?

Possible Answers:

$4,096 \; \textrm{in}^{2}$

$256 \; \textrm{in}^{2}$

$512 \; \textrm{in}^{2}$

It cannot be determined from the information given.

$1,024 \; \textrm{in}^{2}$

Correct answer:

$256 \; \textrm{in}^{2}$

Explanation:

The perimeter of a square is four times its sidelength, so a square with perimeter 64 inches has sides with length 16 inches. Use the area formula:

$A = s^{2} = 16^{2} = 256$

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Example Question #282 : Ssat Middle Level Quantitative (Math)

The area of the square is 81. What is the sum of the lengths of three sides of the square?

Possible Answers:

Correct answer:

Explanation:

A square that has an area of 81 has sides that are the square root of 81 (side² = area for a square). Thus each of the four sides is 9. The sum of three of these sides is 9 + 9 + 9 = 27 .

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Example Question #288 : Ssat Middle Level Quantitative (Math)

The length of one side of a square is $11\: cm$ . What is the square's area?

Possible Answers:

$121\: cm$

$44\: cm^{2}$

$44\: cm$

$121\: cm^{2}$

Correct answer:

$121\: cm^{2}$

Explanation:

The area of any quadrilateral is found by multiplying the length by the width. Because a square has four equal sides, the length and width are the same. For the square in this question, the length and width are $11\: cm$ .

Remember: area is always given in units² .

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Example Question #24 : Quadrilaterals

If a square has a side that is 3 yards long, what is the area in square feet?

Possible Answers:

$30\ \text{ft}^2$

$81\ \text{ft}^2$

$21\ \text{ft}^2$

$9\ \text{ft}^2$

$27\ \text{ft}^2$

Correct answer:

$81\ \text{ft}^2$

Explanation:

The area of a square is found by multiplying the length of a side by itself.

$A=s\times s=s^2$

If one side is 3 yards, this means one side is 9 feet since there are 3 feet in a yard.

$3\ \text{yards}\times3\ \text{feet per yard}=9\ \text{feet}$

Since every side is of equal length, you would multiply 9 feet by 9 feet to find the area.

$A=s\times s$

s=9

$A=9\times9=81$

This results in 81 square feet, which is the correct answer.

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Example Question #161 : Plane Geometry

Find the perimeter of the trapezoid:
Question_12

Possible Answers:

$\small 26$

$\small 21$

$\small 23.5$

$\small 40$

Correct answer:

$\small 21$

Explanation:

The perimeter of any shape is equal to the sum of the lengths of its sides:

$\small P=4+6+3+8=21$

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Example Question #45 : Geometry

The perimeter of a square is . Find the area.

Possible Answers:

424

7744

444

484

Correct answer:

484

Explanation:

A square has four equal sides. Given the value of the perimeter, divide the perimeter by four to determine each side length.

$\frac{88}{4}=22$

Square the side length to find the area since the area of the square is s^2 .

22^2 = 484

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Example Question #1231 : Concepts

Find the area of a square in $\textup{inches}^{2}$ with a side length of $2\textup{ feet}$ .

Possible Answers:

$4\textup{ inches}^{2}$

$144\textup{ inches}^{2}$

$576\textup{ inches}^{2}$

$24\textup{ inches}^{2}$

$48\textup{ inches}^{2}$

Correct answer:

$576\textup{ inches}^{2}$

Explanation:

Write the area for a square.

A=s^2

Convert $\textup{2 feet}$ to inches first. One foot is $\textup{12 inches}$ .

$2 \textup{ feet}(\frac{12\textup{ inches}}{1\textup{ foot}}) = 24\textup{ inches}$

Substitute the side.

$A=(24 \textup{ inches})^2 = 576\textup{ inches}^2$

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Example Question #241 : Ssat Middle Level Quantitative (Math)

The hypotenuse of a right triangle is feet; it has one leg feet long. Give its area in square inches.

Possible Answers:

$101,088 \textrm{ in}^{2}$

$42,120 \textrm{ in}^{2}$

$43,120 \textrm{ in}^{2}$

$77,760 \textrm{ in}^{2}$

$38,880 \textrm{ in}^{2}$

Correct answer:

$38,880 \textrm{ in}^{2}$

Explanation:

The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set c = 39 , b = 36 :

$a^{2} = c^{2} - b^{2}$

$a^{2} = 39 ^{2} - 36^{2}$

$a^{2} = 1,521 - 1,296$

$a^{2} = 225$

$a = \sqrt{225} = 15$

The legs have length and feet; multiply both dimensions by to convert to inches:

$15 \times 12 = 180$ inches

$36 \times 12 = 432$ inches.

Now find half the product:

$A = \frac{1}{2} \cdot 180 \cdot 432 = 38,880\ in^{2}$

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Example Question #51 : Rectangles

Which of the following is equal to the area of a rectangle with length 4.3 meters and width 3.5 meters?

Possible Answers:

$150,500 \textrm{ cm}^{2}$

$15,050 \textrm{ cm}^{2}$

$155,000 \textrm{ cm}^{2}$

$15,500 \textrm{ cm}^{2}$

Correct answer:

$150,500 \textrm{ cm}^{2}$

Explanation:

Multiply each dimension by 100 to convert meters to centimeters:

$4.3 \times 100 = 430$

$3.5 \times 100 = 350$

Multiply these dimensions to get the area of the rectangle in square centimeters:

$430 \times 350 = 150,500\textrm{ cm}^{2}$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #11 : Plane Geometry

Example Question #281 : Ssat Middle Level Quantitative (Math)

Example Question #282 : Ssat Middle Level Quantitative (Math)

Example Question #288 : Ssat Middle Level Quantitative (Math)

Example Question #24 : Quadrilaterals

Example Question #161 : Plane Geometry

Example Question #45 : Geometry

Example Question #1231 : Concepts

Example Question #241 : Ssat Middle Level Quantitative (Math)

Example Question #51 : Rectangles

All HSPT Math Resources

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