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HSPT Math : Concepts

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Example Questions

Example Question #1231 : Concepts

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

Possible Answers:

$21\ \text{ft}^2$

$27\ \text{ft}^2$

$81\ \text{ft}^2$

$9\ \text{ft}^2$

$30\ \text{ft}^2$

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 #1232 : Concepts

Find the perimeter of the trapezoid:
Question_12

Possible Answers:

$\small 21$

$\small 23.5$

$\small 26$

$\small 40$

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 #41 : Geometry

The perimeter of a square is . Find the area.

Possible Answers:

484

444

7744

424

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:

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

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

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

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

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

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 #11 : Triangles

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

Possible Answers:

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

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

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

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

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

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 #161 : Geometry

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

Possible Answers:

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

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

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

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

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

Trapezoid

The above diagram depicts a rectangle RECT with isosceles triangle $\Delta ECM$ . If is the midpoint of $\overline{CT}$ , and the area of the orange region is , then what is the length of one leg of $\Delta ECM$ ?

Possible Answers:

$\sqrt {108}$

$\sqrt {54}$

$\sqrt {96}$

$\sqrt {48}$

Correct answer:

$\sqrt {48}$

Explanation:

The length of a leg of $\Delta ECM$ is equal to the height of the orange region, which is a trapezoid. Call this length/height .

Since the triangle is isosceles, then CM = h , and since is the midpoint of $\overline{CT}$ , MT = h . Also, since opposite sides of a rectangle are congruent,

RE = CT = CM + MT = h + h = 2h

Therefore, the orange region is a trapezoid with bases and and height . Its area is 72, so we can set up and solve this equation using the area formula for a trapezoid:

$\frac{1}{2} (B + b)h = 72$

$\frac{1}{2} (2h + h)h = 72$

$\frac{1}{2} (3h )h = 72$

$\frac{3}{2}h^{2} = 72$

$\frac{3}{2}h^{2} \cdot \frac{2}{3} = 72 \cdot \frac{2}{3}$

$h^{2}= 48$

$h = \sqrt {48}$

This is the length of one leg of the triangle.

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

A trapezoid has a height of inches and bases measuring inches and inches. What is its area?

Possible Answers:

$900\; \textrm{in}^{2}$

$1,500\; \textrm{in}^{2}$

$864\; \textrm{in}^{2}$

$600\; \textrm{in}^{2}$

$750\; \textrm{in}^{2}$

Correct answer:

$750\; \textrm{in}^{2}$

Explanation:

Use the following formula, with B = 36,b = 24,h=25 :

$A = \frac{1}{2} (B+b)h = \frac{1}{2} (36+24) \cdot 25 = 750$

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Example Question #51 : Geometry

What is the area of a triangle with a base of and a height of ?

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a triangle is $\dpi{100} Area=\frac{1}{2}\times base\times height$ .

Plug the given values into the formula to solve:

$\dpi{100} Area=\frac{1}{2}\times 12\times 3$

$\dpi{100} Area=\frac{1}{2}\times 36$

$\dpi{100} Area=18$

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Example Question #1231 : Concepts

Find the area of a square with side length 1.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the area of a square. Thus,

A=s^2=1^2=1

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1231 : Concepts

Example Question #1232 : Concepts

Example Question #41 : Geometry

Example Question #1231 : Concepts

Example Question #11 : Triangles

Example Question #161 : Geometry

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

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

Example Question #51 : Geometry

Example Question #1231 : Concepts

All HSPT Math Resources

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