ISEE Lower Level Quantitative : How to find the area of a square

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

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Example Questions

Example Question #1 : How To Find The Area Of A Square

What is the area of a square if one side of the square is 6?

Possible Answers:

Correct answer:

Explanation:

If one side of a square is 6, then each of the four sides of the square are equal to 6. To find the area of a square, we multiply the length and the height together. The length is 6, and the height is 6, thus the equation we use is .

Remember the formula for the area of a quadrilateral is . For a square, one side is equal to both the length and the width.

Example Question #2 : How To Find The Area Of A Square

One side of a square is  centimeters long. What is the area of the square?

Possible Answers:

Correct answer:

Explanation:

The formula for finding the area of a square is  , or, because this is a square, .

area =  centimeters  centimeters, or 

Example Question #51 : Plane Geometry

A right triangle has a base of  and a height of .

What is the area of the rectangle made by 2 of these triangles aligned along the hypotenuse?

Possible Answers:

Correct answer:

Explanation:

If one combines the 2 identical triangles, their base and height become the length and width of the rectangle.

Area of a rectangle is:

In this case

Example Question #1 : How To Find The Area Of A Square

A square has an area of .  What is the length of one side?

Possible Answers:

\dpi{100} 2\ inches

\dpi{100} 16\ inches

\dpi{100} 8\ inches

\dpi{100} 4\ inches

Correct answer:

\dpi{100} 4\ inches

Explanation:

You can find the area of a square by multiplying two sides together.  All of the sides of a square are equal.  In this case, \dpi{100} 4\times 4=16, so the length of all of the sides of the square is 4 inches.

Example Question #53 : Plane Geometry

Michaela drew th square below.

Screenshot_2015-03-25_at_3.13.25_pm

What is the area of the square?

Possible Answers:

144 square centimeters

48 square centimeters

112 square centimeters

100 square centimeters

12 square centimeters

Correct answer:

144 square centimeters

Explanation:

The area of a square can be found by multiplying the length of a side times itself.  The side length of the above square is 12 cm. By finding 12 x 12, we find that the area of the square is 144 cm. squared.

Example Question #54 : Plane Geometry

James found the area of the square below to be 36 centimeters squared.

Screenshot_2015-03-25_at_3.13.12_pm

What is the length of one side of the square?

Possible Answers:

36 centimeters

18 centimeters

9 centimeters

6 centimeters

8 centimeters

Correct answer:

6 centimeters

Explanation:

The area of a square can be found by multiplying the length of a side by itself.  36 is equal to 6 times 6, therefore the length of one side is 6 centimeters. 

Example Question #4 : How To Find The Area Of A Square

Daphne found the area of the square below to be 81 centimeters squared.

 

Screenshot_2015-03-25_at_3.13.12_pm

What is the length of one side of the square?

 

Possible Answers:

7 centimeters

9 centimeters

8 centimeters

20 centimeters

81 centimeters

Correct answer:

9 centimeters

Explanation:

The area of a square can be found by multiplying the length of a side by itself.  81 is equal to 9 times 9, therefore the length of one side is 9 centimeters. 

 

 

Example Question #56 : Plane Geometry

If the area of a square is , what is the length of each side?

Possible Answers:

Correct answer:

Explanation:

To find the area of a square, the length must be multiplied by the height.  Since a square has four equal sides, the length and width will have the same measurement. We must, therefore, find the square root of .  Since , is the square root of , which makes it the measurement for both the length and the width of the square.

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