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HSPT Math : HSPT Mathematics

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Example Questions

Example Question #392 : Ssat Middle Level Quantitative (Math)

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:

$\sqrt {96}$

$\sqrt {48}$

$\sqrt {108}$

$\sqrt {54}$

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 #1 : 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:

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

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

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

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

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

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 #23 : Area Of A Triangle

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 #1232 : 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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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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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #392 : Ssat Middle Level Quantitative (Math)

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #23 : Area Of A Triangle

Example Question #1232 : Concepts

Example Question #1241 : Concepts

Example Question #1242 : Concepts

Example Question #1243 : Concepts

Example Question #1244 : Concepts

Example Question #1245 : Concepts

Example Question #1246 : Concepts

All HSPT Math Resources

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