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HSPT Math : Concepts

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Example Questions

Example Question #1241 : Concepts

Find the area of a triangle with height 6 and base 3.

Possible Answers:

Correct answer:

Explanation:

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

Given the height is 6 and the base is 3, substitute these values into area of a triangle formula.

Thus,

$A=\frac{1}{2}Bh=\frac{1}{2}*6*3=9$

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Example Question #1242 : Concepts

Square a

What is 60% of the area of the above square?

Possible Answers:

$19\frac{1}{5}$

$\frac{48}{5} \sqrt{2}$

$38\frac{2}{5}$

$\frac{96}{5} \sqrt{2}$

Correct answer:

$19\frac{1}{5}$

Explanation:

The area of a square, it being a rhombus, is the product of the lengths of its diagonals. The diagonals are of the same length, so both diagonals have length 8, and the area of the square is

$\frac{1}{2} \times 8^{2} = \frac{1}{2} \times 8 \times 8 = 32$ .

60% of 32 is equal to 32 multiplied by $\frac{60}{100}$ , which is

$32 \times \frac{60}{100} = 32 \times \frac{3}{5} = 19\frac{1}{5}$ .

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Example Question #1243 : Concepts

A circle has radius 12. Which of the following gives 40% of the area of this circle?

Possible Answers:

$\frac{72 \pi}{5}$

$\frac{144 \pi}{5}$

$\frac{576 \pi}{5}$

$\frac{288 \pi}{5}$

Correct answer:

$\frac{288 \pi}{5}$

Explanation:

The area of a circle with radius is

$A = \pi r^{2}$ .

The radius of the circle is r=12 , so the area is

$A = \pi \cdot 12^{2} = 144 \pi$ .

40% of this is

$144 \pi \cdot \frac{40}{100} = 144 \pi \cdot \frac{2}{5 }= \frac{288 \pi}{5}$

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Example Question #1244 : Concepts

A rectangle measures six feet in width and four and one-half feet in height. Give its area in square yards.

Possible Answers:

9 square yards

81 square yards

3 square yards

243 square yards

Correct answer:

3 square yards

Explanation:

Convert each dimension from feet to yards by dividing by conversion factor 3:

$6 \textup{ ft} \div 3 \textup{ yd/ft} = 2 \textup{ yd}$

$4 \frac{1}{2} \textup{ ft} \div 3 \textup{ yd/ft} = \frac{9}{2} \textup{ ft} \div 3 \textup{ yd/ft}= \frac{3}{2} \textup{ yd}$

Their product is the area in square yards:

$2 \textup{ yd} \times \frac{3}{2} \textup{ yd} = 3 \textup{ yd} ^{2}$ .

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Example Question #1245 : Concepts

Rectangle 2

Note: Figure NOT drawn to scale.

The above rectangle has a perimeter of 20. Give its area.

Possible Answers:

$18\frac{21}{26}$

$9\frac{21}{52}$

$54 \frac{7}{16}$

$21 \frac{15}{16}$

Correct answer:

$21 \frac{15}{16}$

Explanation:

The perimeter of a rectangle, given length and width , is

P = 2 (L+W)

We can find missing dimension by setting P= 20 and $W = 3 \frac{1}{4}$ :

$20 = 2 \left (L+ 3 \frac{1}{4} \right )$

$20 \div 2 = 2 \left (L+ 3 \frac{1}{4} \right ) \div 2$

$10= L+ 3 \frac{1}{4}$

$10- 3 \frac{1}{4} = L+ 3 \frac{1}{4} - 3 \frac{1}{4}$

$6 \frac{3}{4} = L$

To find the area, multiply the length and the width:

$6 \frac{3}{4} \times 3 \frac{1}{4} = \frac{27}{4} \times \frac{13}{4} = \frac{351}{16} = 21 \frac{15}{16}$ .

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Example Question #1246 : Concepts

A circle has circumference $\frac{16 }{25}\pi$ . Give its area.

Possible Answers:

$\frac{4}{5} \pi$

$\frac{8}{5} \pi$

$\frac{64}{625} \pi$

$\frac{256}{625} \pi$

Correct answer:

$\frac{64}{625} \pi$

Explanation:

The radius of a circle is its circumference divided by $2 \pi$ :

$r =C \div 2 \pi = \frac{16 }{25}\pi \div 2 \pi = \frac{16 \pi }{25} \cdot \frac{1}{2 \pi} = \frac{8}{25}$

The area of a circle, given its radius , is

$A = \pi r^{2}$

Setting $r = \frac{8}{25}$ :

$A = \pi \left ( \frac{8}{25} \right )^{2} = \frac{64}{625} \pi$

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Example Question #1247 : Concepts

Rectangle 2

The above rectangle has perimeter 100. Give its area in terms of .

Possible Answers:

$50 N - N^{2}$

$100 N - N^{2}$

$2N + \frac{200}{N}$

$N + \frac{100}{N}$

Correct answer:

$50 N - N^{2}$

Explanation:

If we let be the width of the rectangle, then the perimeter can be given as the sum of the sidelengths, which is

W + N + W + N = 2W + 2N

If we set this equal to 100, then we can solve for in terms of as follows:

2W + 2N = 100

2W + 2N - 2N = 100 - 2N

2W = 100 - 2N

$\frac{2W}{2} = \frac{100 - 2N}{2}$

W = 50 - N

Multiply this width by length to get the area:

$N (50 - N)= 50 N - N^{2}$

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Example Question #1841 : Hspt Mathematics

Square a

The area of the above square is 40% of what number?

Possible Answers:

360

19.2

57.6

120

Correct answer:

360

Explanation:

The area of a square with sides of length 12 is the square of 12, or

$12 ^{2} = 12 \times 12 = 144$

The number of which 144 is 40% can be found by dividing 144 by 40%, or $\frac{40}{100}$ :

$144 \div \frac{40}{100}= 144 \times \frac{100}{40} = 360$ .

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Example Question #4 : How To Find The Area Of A Rectangle

What is the area of the figure below?

Possible Answers:

32in^2

22in^2

10in^2

12in^2

28in^2

Correct answer:

22in^2

Explanation:

To find the area of the figure above, we need to slip the figure into two rectangles.

11.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=6\times 2$ $A=5\times 2$

A=12in^2 A=10in^2

To find our final answer, we need to add the areas together.

12in^2+10in^2=22in^2

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Example Question #5 : How To Find The Area Of A Rectangle

What is the area of the figure below?

Possible Answers:

40in^2

28in^2

18in^2

32in^2

14in^2

Correct answer:

32in^2

Explanation:

To find the area of the figure above, we need to slip the figure into two rectangles.

10.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=7\times 2$ $A=6\times 3$

A=14in^2 A=18in^2

To find our final answer, we need to add the areas together.

14in^2+18in^2=32in^2

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1241 : Concepts

Example Question #1242 : Concepts

Example Question #1243 : Concepts

Example Question #1244 : Concepts

Example Question #1245 : Concepts

Example Question #1246 : Concepts

Example Question #1247 : Concepts

Example Question #1841 : Hspt Mathematics

Example Question #4 : How To Find The Area Of A Rectangle

Example Question #5 : How To Find The Area Of A Rectangle

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