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HSPT Math : Geometry

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Example Questions

Example Question #282 : Plane Geometry

Square X has 3 times the area of Square Y. If the perimeter of Square Y is 24 ft, what is the area of Square X, in sq ft?

Possible Answers:

144

112

108

Correct answer:

108

Explanation:

Find the area of Square Y, then calculate the area of Square X.

If the perimeter of Square Y is 24, then each side is 24/4, or 6.

A = 6 * 6 = 36 sq ft, for Square Y

If Square X has 3 times the area, then 3 * 36 = 108 sq ft.

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Example Question #254 : Geometry

A square has an area of $36 in^{2}$ . If the side of the square is reduced by a factor of two, what is the perimeter of the new square?

Possible Answers:

$32\ in.$

$12\ in.$

$16\ in.$

$48\ in.$

$24\ in.$

Correct answer:

$12\ in.$

Explanation:

The area of the given square is given by $A = s^{2}$ so the side must be 6 in. The side is reduced by a factor of two, so the new side is 3 in. The perimeter of the new square is given by $P = 4s = 4\cdot 3 = 12 in$ .

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Example Question #1 : How To Find The Perimeter Of A Rectangle

A rectangle has a width of 2x. If the length is five more than 150% of the width, what is the perimeter of the rectangle?

Possible Answers:

5x + 10

6x² + 5

10(x + 1)

5x + 5

6x² + 10x

Correct answer:

10(x + 1)

Explanation:

Given that w = 2x and l = 1.5w + 5, a substitution will show that l = 1.5(2x) + 5 = 3x + 5.

P = 2w + 2l = 2(2x) + 2(3x + 5) = 4x + 6x + 10 = 10x + 10 = 10(x + 1)

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Example Question #1 : Parallelograms

ABCD is a parallelogram. BD = 5. The angles of triangle ABD are all equal. What is the perimeter of the parallelogram?

Figure_1

Possible Answers:

$10\sqrt{3}$

$15\sqrt{3}$

$11\sqrt{2}$

Correct answer:

Explanation:

If all of the angles in triangle ABD are equal and line BD divides the parallelogram, then all angles in triangle BDC must be equal as well.

We now have two equilateral triangles, so all sides of the triangles will be equal.

All sides therefore equal 5.

5+5+5+5 = 20

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Example Question #131 : Geometry

A square has a length of $19\textup{ feet}$ . What is the perimeter in inches?

Possible Answers:

$894\textup{ inches}$

$912\textup{ inches}$

$67\textup{ inches}$

$\frac{19}{3}\textup{ inches}$

$76\textup{ inches}$

Correct answer:

$912\textup{ inches}$

Explanation:

The square perimeter is $\textup{4 times}$ the side length.

P=4s

Substitute and multiply to find the perimeter.

$P=4(19\textup{ feet})= 76 \textup{ feet}$

There are $\textup{12 inches}$ in $\textup{1 foot}$

Multiply the perimeter with .

$76 \textup{ feet} (\frac{12 \textup{ inches}}{1 \textup{ foot}}) = 912 \textup{ inches}$

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Example Question #83 : Plane Geometry

Rectangle

Give the perimeter of the above rectangle in centimeters, using the conversion factor 91.44 centimeters per yard.

Possible Answers:

$2,011.68 \textrm{ cm}$

$1,097.28 \textrm{ cm}$

$2,194.56 \textrm{ cm}$

$1,005.84 \textrm{ cm}$

$4,389.12 \textrm{ cm}$

Correct answer:

$2,011.68 \textrm{ cm}$

Explanation:

The perimeter of the rectangle is 8 + 3 + 8 + 3 = 22 yards. To convert this to centimeters, multiply by the given conversion factor:

$91.44 \times 22 = 2,011.68$ centimeters.

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Example Question #131 : Geometry

Find the perimeter of a rectange with length 9 and width 4.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter of a rectangle.

Given the length of the rectangle is 9 and the width is 4; substitute these values into the perimeter equation.

Thus,

P=2(l+w)=2*(9+4)=2*13=26

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Example Question #1913 : Hspt Mathematics

A square has perimeter 20. Which of the following gives 75% of the length of one of its diagonals?

Possible Answers:

$\frac{15\sqrt{3}}{4}$

$\frac{15\sqrt{2}}{4}$

$\frac{15\sqrt{3}}{2}$

$\frac{15\sqrt{2}}{2}$

Correct answer:

$\frac{15\sqrt{2}}{4}$

Explanation:

The length of one side of a square is one-fourth of its perimeter, which here makes its length

$\frac{1}{4} \cdot 20 = 5$ .

The length of a diagonal of a square is $\sqrt{2}$ times this sidelength, so the square has diagonals of length $5 \sqrt{2}$ .

75% of this is

$5 \sqrt{2} \cdot \frac{75}{100} = \frac{5 \sqrt{2}}{1} \cdot \frac{3}{4} = \frac{15 \sqrt{2}}{4}$ .

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Example Question #132 : Geometry

A circle has radius 8. Which of the following gives 60% of the circumference of this circle?

Possible Answers:

$\frac{96 \pi }{5}$

$\frac{24 \pi }{5}$

$\frac{192\pi }{5}$

$\frac{48 \pi }{5}$

Correct answer:

$\frac{48 \pi }{5}$

Explanation:

The circumference of a circle is its radius mulitplied by $2 \pi$ . The radius is 8, so the circumference is

$8 \cdot 2 \pi = 16 \pi$ .

60% of this is

$16 \pi \cdot \frac{60}{100}= 16 \pi \cdot \frac{3}{5} = \frac{48 \pi }{5}$

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Example Question #133 : Geometry

Rectangle 2

Note: Figure NOT drawn to scale.

The above rectangle has area 18. Give its perimeter.

Possible Answers:

$18\frac{11}{16}$

$8\frac{41}{52}$

$47\frac{15}{16}$

$17\frac{15}{26}$

Correct answer:

$17\frac{15}{26}$

Explanation:

The product of the length and the width of a rectangle is its area, so to find the length, divide the area by the width:

$L = A \div W = 18 \div 3\frac{1}{4} = \frac{18}{1} \div \frac{13}{4} = \frac{18}{1} \cdot \frac{4} {13} = \frac{72}{13}$

We can use $L = \frac{72}{13}$ and $W = 3\frac{1}{4} = \frac{13}{4}$ to find the perimeter by adding each of these twice:

$P = \frac{72}{13} + \frac{13}{4} + \frac{72}{13} + \frac{13}{4}$

$P = \frac{288}{52} + \frac{169}{52} +\frac{288}{52} + \frac{169}{52}$

$P = \frac{914}{52} = \frac{457}{26} = 17\frac{15}{26}$

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HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #282 : Plane Geometry

Example Question #254 : Geometry

Example Question #1 : How To Find The Perimeter Of A Rectangle

Example Question #1 : Parallelograms

Example Question #131 : Geometry

Example Question #83 : Plane Geometry

Example Question #131 : Geometry

Example Question #1913 : Hspt Mathematics

Example Question #132 : Geometry

Example Question #133 : Geometry

All HSPT Math Resources

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