Pre-Algebra : Geometry

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #1 : Geometry

Betty needs to buy carpeting to cover her entire bedroom floor, which is 12 ft. long and 8 ft. wide. How much carpeting does she need to buy?

Possible Answers:

Correct answer:

Explanation:

Remember to use the formula below to find area:

\displaystyle Area=length\cdot width

Since Betty needs carpeting to cover her floor, this problem asks you to find the area. This means you need to multiply length and width to find the area, which is given in square feet, since each foot of carpeting is not only one foot long, but also one foot wide (a square).

Step 1: plug in the numbers for length and width

\displaystyle Area=12\cdot8

Step 2: solve

\displaystyle Area=96 sq. ft.

Example Question #2 : Geometry

Untitled

The rectangle in the above figure has length 20 and height 10. What is the area of the red region?

Possible Answers:

\displaystyle 150

\displaystyle 200 - 5 \pi

\displaystyle 175

Insufficient information is given to determine the area.

\displaystyle 200 - \frac{5}{2} \pi

Correct answer:

\displaystyle 175

Explanation:

The red region is formed by removing a triangle from a rectangle.

The rectangle measures 20 by 10, and, subsequently, has area

\displaystyle 20 \cdot 10 = 200.

The triangle has base 10. Its height is the radius of the circle, which is 5, so its area is 

\displaystyle \frac{1}{2} \cdot 10 \cdot 5 = 25.

The difference between the areas, which is the area of the red region, is \displaystyle 200 - 25 = 175.

Example Question #3 : Geometry

Untitled_2

The rectangle in the above figure has length 20 and height 10. What is the area of the red region?

Possible Answers:

\displaystyle 200 + \frac{5}{2} \pi

\displaystyle 225

Insufficient information is given to determine the area.

\displaystyle 250

\displaystyle 200 + 5 \pi

Correct answer:

\displaystyle 225

Explanation:

The red region is a composite of two figures:

One is a rectangle measuring 20 by 10, which, subsequently, has area

\displaystyle 20 \cdot 10 = 200.

The other is a triangle with base 10. Its height is the radius of the circle, which is 5, so its area is 

\displaystyle \frac{1}{2} \cdot 10 \cdot 5 = 25.

The sum of the areas, which is the area of the red region, is \displaystyle 200 + 25 = 225.

Example Question #4 : Geometry

Thompson High School wants to buy artificial turf for their practice soccer field. The field is 150 ft by 100 ft. How much turf should they buy?

Possible Answers:

 

Correct answer:

 

Explanation:

Recall, the area of a rectangle = length x width

Next, plug in the two values given in the problem

\displaystyle \small Area = 150 *100 = 15000

Example Question #5 : Geometry

Judy needs to buy a glass table cover for a dinner party, which is 8 ft. long and 3 ft. wide. How much glass does she need to buy?

Possible Answers:

Correct answer:

Explanation:

Explanation:

Remember to use the formula below to find area:

\displaystyle Area = length\cdot width

Since Judy needs enough glass to cover the whole table, this problem asks you to find the area. This means you need to multiply length and width to find the area, which is given in square feet, since each foot of glass is not only one foot long, but also one foot wide (a square).

Step 1: Plug in the numbers for the length and width

\displaystyle Area = 8 \cdot 3

Step 2: Solve

\displaystyle Area = 24 sq. ft.

Example Question #6 : Geometry

Jessica's blanket is 12 square feet. Lisa has a blanket that is half the size of Jessica's blanket. Which of the following are possible dimensions of Lisa's blanket?

Possible Answers:

\displaystyle 3\ ft\times3\ ft

\displaystyle 3\ ft\times2\ ft

\displaystyle 2\ ft\times2\ ft

\displaystyle 1\ ft\times12\ ft

Correct answer:

\displaystyle 3\ ft\times2\ ft

Explanation:

The area of a rectangle if found by multiplying the length times the width. Here, we know that Lisa's blanket is half the area of Jessica's blanket. Since Jessica's blanket is 12 square feet, that means that Lisa's blanket must be 6 square feet. 

The only length and width values that give us 6 square feet when multiplied by one another are 3 feet by 2 feet. This is therefore the correct answer. 

Example Question #7 : Geometry

Jon built a new garden with two sides equalling , and the other sides equalling . What is the area of Jon's new garden?

Possible Answers:

Correct answer:

Explanation:

In order to do this problem you must imagine the garden as a rectangle with sides of \displaystyle 10ft by \displaystyle 15ft by \displaystyle 10ft by \displaystyle 15ft.

 

The formula for area of a rectangle is \displaystyle A=l\cdot w.

In our case the length is 10 and the width is 15. To find the area of a rectangle you must multiply \displaystyle 10ft by \displaystyle 15ft, which equals \displaystyle 150ft^2

Example Question #136 : Geometry

The area of the following rectangle is \displaystyle 48\: cm^2. Solve for \displaystyle x.

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Possible Answers:

\displaystyle x=16

\displaystyle x=8

\displaystyle x=12

\displaystyle x=4

Correct answer:

\displaystyle x=4

Explanation:

The area of a rectangle can be found by multiplying the length by the width.

\displaystyle A=l\times w

\displaystyle 48=3x\times x=3x^2

\displaystyle 48=3x^2

\displaystyle \frac{48}{3}=\frac{3x^2}{3}

\displaystyle 16=x^2

\displaystyle \sqrt{16}=\sqrt{x^2}

\displaystyle 4=x

Example Question #3 : Area

A square has a perimeter of \displaystyle 16in. What is its area?

Possible Answers:

\displaystyle 16in^2

\displaystyle 4in^2

\displaystyle 8in^2

\displaystyle 64in^2

Correct answer:

\displaystyle 16in^2

Explanation:

A square with a perimeter of \displaystyle 16in has \displaystyle 4 equal sides whose lengths add up to \displaystyle 4. You could figure out what these sides have to be in a lot of different ways. If you use algebra, you might set up an equation like \displaystyle x+x+x+x=16 or \displaystyle 4x=16. You would figure out that the side lengths must all be \displaystyle 4. If a square has side lengths of \displaystyle 4 inches, to figure out the area you would do \displaystyle 4*4, or \displaystyle 4^2, and you would get an answer of \displaystyle 16.

Example Question #4 : Area

A square has a perimeter of \displaystyle 76 cm. What is its area?

Possible Answers:

\displaystyle 152cm^{2}

\displaystyle 76cm^{2}

\displaystyle 361 cm^{2}

Not enough information given to solve.

\displaystyle 38cm^{2}

Correct answer:

\displaystyle 361 cm^{2}

Explanation:

A square has a perimeter of \displaystyle 76 cm. The four sides of any square are equal in length, so to find one side of the square, we divide the perimeter by \displaystyle 4.

\displaystyle 76cm \div4=19 cm  

The area of a square is length x width, and in this case \displaystyle 1 side x \displaystyle 1 side:

 

\displaystyle 19cm \times 19cm = 361cm^{2}

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