Pre-Algebra : Area of a Rectangle or Square

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

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Example Question #1 : Area Of A Rectangle Or Square

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:

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

Step 2: solve

Example Question #2 : Area Of A Rectangle Or Square

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

Possible Answers:

Insufficient information is given to determine the area.

Correct answer:

Explanation:

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

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

.

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

.

The difference between the areas, which is the area of the red region, is .

Example Question #3 : Area

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

Possible Answers:

Insufficient information is given to determine the area.

Correct answer:

Explanation:

The red region is a composite of two figures:

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

.

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

.

The sum of the areas, which is the area of the red region, is .

Example Question #3 : Area Of A Rectangle Or Square

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

Example Question #5 : Area

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:

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

Step 2: Solve

Example Question #4 : 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:

Correct answer:

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 #4 : Area Of A Rectangle Or Square

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  by  by  by .

 

The formula for area of a rectangle is .

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

Example Question #3 : How To Find The Area Of A Rectangle

The area of the following rectangle is . Solve for .

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Possible Answers:

Correct answer:

Explanation:

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

Example Question #6 : Geometry

A square has a perimeter of . What is its area?

Possible Answers:

Correct answer:

Explanation:

A square with a perimeter of has  equal sides whose lengths add up to . 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 or . You would figure out that the side lengths must all be . If a square has side lengths of  inches, to figure out the area you would do , or , and you would get an answer of .

Example Question #5 : Area Of A Rectangle Or Square

A square has a perimeter of . What is its area?

Possible Answers:

Not enough information given to solve.

Correct answer:

Explanation:

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

  

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

 

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