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

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Question

A square has an area of $16\ in^{2}$ . What is the length of one side?

Answer

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.

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Question

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

Answer

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.

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Question

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?

Answer

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

Area of a rectangle is:

$length\times height$

In this case

$7\times 4=28$

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Question

If the area of a square is $\small 36 ft^{2}$ , what is the length of each side?

Answer

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 $\small 36$ . Since $\small 6\cdot 6=36$ , $\small 6$ is the square root of $\small 36$ , which makes it the measurement for both the length and the width of the square.

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Question

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

Answer

The formula for finding the area of a square is $area = base\times height$ , or, because this is a square, $area = side^{2}$ .

area = centimeters $\times 4$ centimeters, or $16: cm^{2}$

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Question

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

What is the length of one side of the square?

Answer

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.

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Question

Michaela drew th square below.

What is the area of the square?

Answer

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.

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Question

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

What is the length of one side of the square?

Answer

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.

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Question

Find the area of a square whose side length is .

Answer

To solve, simply use the formula for are of a square. Thus,

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Question

Find the area of a square with side length .

Answer

To solve, simply use the formula for the area of a square. Thus,

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Question

If the perimeter of a square is 18 cm, what must the area of this square be?

Answer

Remember that a square has four sides, each side with equal lengths. If a square has a perimeter of 18 cm, that means that each side has a length of

18 ÷ 4 =

4.5 cm.

The formula for the area of a square is length x width or length squared (length x length), since each side of a square has the same length.

So,

4.5 x 4.5 =

20.25cm2

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Question

What is the area of a square that has a side with a length of 9 cm?

Answer

The area of a square can be found using the same equation as the area of a rectangle - length times width.

$A=l\times w$

However, in the case of a square, all of the sides are of equal length. Therefore, the area of a square can be found using the equation:

$A=l\times l$ or

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Question

What is the area of a square that has a side with a length of 10 in.?

Answer

To calculate the area of a square, you need to multiply the length by the width. By definition, a square has 4 equal sides. So, by knowing the length of one side of the square, you know the length measurement and the width measurement.

Since the length of one side of this square is 10 in., you would multiply to get the answer.

Because area is the number of squares that would be used to cover the inside the shape, it is given in units2. As a result, the answer is 100 in.2.

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Question

What is the area of a square with a side that measures feet?

Answer

The area of a square can be found using the following formula:

$A=s^{^{2}}$

The side measures feet.

$5^{2}=25$

Therefore, the area of the square is square feet.

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Question

If the perimeter of a square is 48 inches, what is the area?

Answer

The perimeter of a square is given by , where is the sidelength.

Plug in the given value for the perimeter:

Divide both sides by 4 to find the sidelength:

The area of a square is given by $A=s^{2}$ .

Plug in the sidelength we just calculated to find the area:

$A=s^{2}=(12)^{2}=144; in^{2}$

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Question

If the perimeter of a square is 40 centimeters, what is the area?

Answer

The perimeter of a square is given by , where is the sidelength.

We know the perimeter, so we can set up an equation to find the sidelength:

Divide both sides by 4 to isolate the sidelength:

The area of a square is given by $A=s^{2}$ .

We just calculated the sidelength, so now we can find the area:

$A=s^{2}=(10)^{2}=100; cm^{2}$

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Question

The perimeter of a square is . What is the area?

Answer

The perimeter of a square is given by , or . Divide by four to get .

The area of a square is given by $A=s^{2}$ . Substitute the value obtained from the perimeter equation to get $A=s^{2}=(12)^{2}=144 ; in^{2}$ .

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Question

The perimeter of a square is . What is the area?

Answer

The perimeter of a square is given by , or . Divide by four to get .

The area of a square is given by $A=s^{2}$ . Substitute the side length obtained from the perimeter equation to get $A=s^{2}=(5)^{2}=25 ; in^{2}$ .

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Question

The perimeter of a square is . What is the area?

Answer

The perimeter of a square is given by . Here , so divide by four to get .

The area of a square is given by $A=s^{2}$ . Substitute the side length obtained from the perimeter equation to get $A=s^{2}=(8)^{2}=64 ; cm^{2}$ .

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Question

The perimeter of a square is . What is the area?

Answer

The perimeter of a square is given by , or . Divide by four to get .

The area of a square is given by $A=s^{2}$ . Substitute the side length obtained from the perimeter equation to get $A=s^{2}=(6)^{2}=36 ; cm^{2}$ .

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