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HSPT Math : Geometry

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Example Questions

Example Question #61 : Geometry

Rectangle 2

Note: Figure NOT drawn to scale.

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

Possible Answers:

$21 \frac{15}{16}$

$54 \frac{7}{16}$

$18\frac{21}{26}$

$9\frac{21}{52}$

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 #62 : Geometry

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

Possible Answers:

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

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

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

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

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 #61 : Geometry

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 #2 : Find Areas Of Rectilinear Figures: Ccss.Math.Content.3.Md.C.7d

What is the area of the figure below?

Possible Answers:

10in^2

32in^2

22in^2

28in^2

12in^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 #64 : Geometry

What is the area of the figure below?

Possible Answers:

28in^2

32in^2

14in^2

40in^2

18in^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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Example Question #62 : Geometry

What is the area of the figure below?

Possible Answers:

112in^2

100in^2

96in^2

24in^2

72in^2

Correct answer:

96in^2

Explanation:

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

9.5

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

$A=9\times 8$ $A=8\times 3$

A=72in^2 A=24in^2

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

72in^2+24in^2=96in^2

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Example Question #1 : Find Areas Of Rectilinear Figures: Ccss.Math.Content.3.Md.C.7d

What is the area of the figure below?

Possible Answers:

32in^2

28in^2

24in^2

8in^2

12in^2

Correct answer:

32in^2

Explanation:

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

8.5

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

$A=4\times 6$ $A=4\times 2$

A=24in^2 A=8in^2

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

24in^2+8in^2=32in^2

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Example Question #2 : Find Areas Of Rectilinear Figures: Ccss.Math.Content.3.Md.C.7d

What is the area of the figure below?

Possible Answers:

18in^2

25in^2

36in^2

34in^2

9in^2

Correct answer:

34in^2

Explanation:

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

7.5

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

$A=5\times 5$ $A=3\times 3$

A=25in^2 A=9in^2

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

25in^2+9in^2=34in^2

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Example Question #1241 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

What is the area of the figure below?

Possible Answers:

8in^2

48in^2

40in^2

36in^2

44in^2

Correct answer:

44in^2

Explanation:

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

6.5

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

$A=4\times 2$ $A=9\times 4$

A=8in^2 A=36in^2

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

8in^2+36in^2=44in^2

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HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #61 : Geometry

Example Question #62 : Geometry

Example Question #1247 : Concepts

Example Question #61 : Geometry

Example Question #2 : Find Areas Of Rectilinear Figures: Ccss.Math.Content.3.Md.C.7d

Example Question #64 : Geometry

Example Question #62 : Geometry

Example Question #1 : Find Areas Of Rectilinear Figures: Ccss.Math.Content.3.Md.C.7d

Example Question #2 : Find Areas Of Rectilinear Figures: Ccss.Math.Content.3.Md.C.7d

Example Question #1241 : Isee Lower Level (Grades 5 6) Quantitative Reasoning

All HSPT Math Resources

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