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HSPT Math : Geometry

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Example Question #51 : Geometry

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

Possible Answers:

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

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

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

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

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

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 #28 : How To Find The Area Of A Rectangle

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

Possible Answers:

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

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

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

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

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 #213 : Geometry

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:

$\sqrt {96}$

$\sqrt {48}$

$\sqrt {54}$

$\sqrt {108}$

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 #214 : Geometry

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

Possible Answers:

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

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

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

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

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

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 #101 : 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 #51 : Geometry

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 #52 : Geometry

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 #51 : Geometry

Square a

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

Possible Answers:

$19\frac{1}{5}$

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

$38\frac{2}{5}$

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

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 #51 : Geometry

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 #53 : Geometry

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

Possible Answers:

3 square yards

9 square yards

243 square yards

81 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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HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #51 : Geometry

Example Question #28 : How To Find The Area Of A Rectangle

Example Question #213 : Geometry

Example Question #214 : Geometry

Example Question #101 : Geometry

Example Question #51 : Geometry

Example Question #52 : Geometry

Example Question #51 : Geometry

Example Question #51 : Geometry

Example Question #53 : Geometry

All HSPT Math Resources

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