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High School Math : Geometry

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Example Questions

Example Question #575 : High School Math

The ratio of the areas of two rectangles is 6:1 . If the larger rectangle has a length of and a width of , what is the area of the smaller rectangle?

Possible Answers:

units squared

Correct answer:

units squared

Explanation:

The area of the larger rectangle is calculated as $6\times 3 = 18$ units squared. Since the ratio of the larger to the smaller rectangle is 6:1 , dividing the larger rectangle's area by gives the area of the smaller rectangle:

$\frac{18}{6} = 3$ units squared

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Example Question #33 : Rectangles

Joey is working in his yard. In the middle of his $80\; ft\; by\; 40\; ft$ rectangular yard he places a round cement fountain. The fountain has a diameter of $18\; ft$ . One bag of grass seed covers 250 square feet. How many bags of grass seed will Joey need to cover his yard?

Possible Answers:

Correct answer:

Explanation:

First, find the area of the rectangular yard:

l*w=80*40=3200 square feet

Next, find the area of the round cement fountain:

$\pi r^{2}=\pi (9)^{2}\approx 3.14(9)^{2}\approx 254$ square feet

Then find the difference between the two:

3200-254=2946 square feet

Now, to get the number of grass seed bags needed, divide the area by 250 to get approximately 11.75 bags. Because one can't purchase a partial bag, the correct answer is the next largest whole number, or bags of grass seed.

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Example Question #2 : Rectangles

A rectangle has a perimeter of 40 inches. It is 3 times as long as it is wide. What is the area of the rectangle in square inches?

Possible Answers:

Correct answer:

Explanation:

The width of the rectangle is w, therefore the length is 3w. The perimeter, P, can then be described as P = w + w + 3w +3w

40 = 8w

w = 5

width = 5, length = 3w = 15

A = 5*15 = 75 square inches

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Example Question #1 : Rectangles

Angela is carpeting a rectangular conference room that measures 20 feet by 30 feet. If carpet comes in rectangular pieces that measures 5 feet by 4 feet, how many carpet pieces will she need to carpet the entire room?

Possible Answers:

600

Correct answer:

Explanation:

First, we need to find the area of the room. Because the room is rectangular, we can multiply 20 feet by 30 feet, which is 600 square feet. Next, we need to know how much space one carpet piece covers. Because the carpet pieces are also rectangular, we can multiply 4 feet by 5 feet to get 20 feet. To determine how many pieces of carpet Angela will need, we must divide the total square footage of the room (600 feet) by the square footage covered by one carpet piece (20 feet). 600 divided by 20 is 30, so Angela will need 30 carpet pieces to carpet the entire room.

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Example Question #221 : Geometry

If the width of a rectangle is 8 inches, and the length is half the width, what is the area of the rectangle in square inches?

Possible Answers:

Correct answer:

Explanation:

the length of the rectangle is half the width, and the width is 8, so the length must be half of 8, which is 4.

The area of the rectangle can be determined from multiplying length by width, so,

4 x 8 = 32 inches squared

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Example Question #2 : Rectangles

If Mrs. Stietz has a patio that measures 96 inches by 72 inches and she wants to cover it with stone tiles that measure one foot by half a foot, what is the minimum number of tiles she needs to cover the patio?

Possible Answers:

6912

Correct answer:

Explanation:

96. Converting the dimensions of the tiles to inches, they each measure 12 inches by 6 inches. This means that there need to be 8 tiles to span the length of the patio, and 6 tiles to span the width of the patio. She needs to cover the entire area, so we can multiply 8 times 12 to get 96, the number of tiles she needs for the patio.

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Example Question #181 : Sat Mathematics

The front façade of a building is 100 feet tall and 40 feet wide. There are eight floors in the building, and each floor has four glass windows that are 8 feet wide and 6 feet tall along the front façade. What is the total area of the glass in the façade?

Possible Answers:

192 ft²

768 ft²

1536 ft²

2464 ft²

1536 ft²

Correct answer:

1536 ft²

Explanation:

Glass Area per Window = 8 ft x 6 ft = 48 ft²

Total Number of Windows = Windows per Floor * Number of Floors = 4 * 8 = 32 windows

Total Area of Glass = Area per Window * Total Number of Windows = 48 * 32 = 1536 ft²

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Example Question #41 : Rectangles

Mark is making a plan to build a rectangular garden. He has 160 feet of fence to form the outside border of the garden. He wants the dimensions to look like the plan outlined below:

Screen_shot_2013-03-19_at_9.17.30_pm

What is the area of the garden, rounded to the nearest square foot?

Possible Answers:

160

486

126

1472

Correct answer:

1472

Explanation:

Perimeter: Sum of the sides:

4x + 4x + 2x+8 +2x+8 = 160

12x + 6 = 160

12x = 154

x = $\frac{77}{6}$

Therefore, the short side of the rectangle is going to be:

$\dpi{100} \dpi{100} 2\cdot \frac{77}{6}+3=\frac{172}{6}=\frac{86}{3}$

And the long side is going to be:

$\dpi{100} 4\cdot \frac{77}{6}=\frac{308}{6}=\frac{154}{3}$

The area of the rectangle is going to be as follows:

Area = lw

$\dpi{100} Area = \frac{86}{3}\cdot \frac{154}{3}=\frac{13,244}{9}=1471.55\approx 1472\ ft^{2}$

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Example Question #651 : Psat Mathematics

Two circles of a radius of {2}'' each sit inside a square with a side length of {8}'' . If the circles do not overlap, what is the area outside of the circles, but within the square?

Possible Answers:

$64-8\pi$

$36-4\pi$

$16+8\pi$

$36-8\pi$

$36-6\pi$

Correct answer:

$64-8\pi$

Explanation:

The area of a square = $\dpi{100} \small side^{2}$

The area of a circle is $\dpi{100} \small \pi r^{2}$

Area = Area of Square $\dpi{100} \small -$ 2(Area of Circle) =

$8^{2}-2\cdot \pi (2)^{2}$

$64-8\pi$

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Example Question #51 : Quadrilaterals

If the area Rectangle A is $25\%$ larger than Rectangle B and the sides of Rectangle A are and , what is the area of Rectangle B?

Possible Answers:

Correct answer:

Explanation:

$A = \text{length}\: \times \:\text{width} = 10 \times 6 = 60$

A = 1.25 B

60 = 1.25B

$B =\frac{60}{1.25} = 48$

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High School Math : Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #575 : High School Math

Example Question #33 : Rectangles

Example Question #2 : Rectangles

Example Question #1 : Rectangles

Example Question #221 : Geometry

Example Question #2 : Rectangles

Example Question #181 : Sat Mathematics

Example Question #41 : Rectangles

Example Question #651 : Psat Mathematics

Example Question #51 : Quadrilaterals

All High School Math Resources

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