How to find the area of a square - ISEE Middle Level Math

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Question

What is the area of a square with a side length of 4?

Answer

The area of a square is represented by the equation $\dpi{100} Area = side^{2}$ .

Therefore the area of this square is $\dpi{100} 4^{2}=16$ .

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Question

Square A has sides measuring 5 meters. A second square, Square B, has sides that are 2 meters longer than the sides of Square A. What is the difference in area of Square A and Square B?

Answer

The area of Square A is 5 * 5, or 25 m2.

Since each of Square B's sides is 2 meters longer, the sides measure 7 meters. Therefore, the area of square B is 49 m2.

Subtract to find the difference in areas: $49-25=24\ m^2$

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Question

Which of the following is equal to the area of a square with perimeter 8 meters?

Answer

The sidelength of a square is one-fourth its perimeter, so the sidelength here is one-fourth of 8, or 2, meters. One meter is equal to 100 centimeters, so the sidelength is 200 centimeters. Square this to get the area:

$200 ^{2} = 200 \times 200 = 40,000$ square centimeters.

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Question

Which of the following is the area of a square with perimeter 7 feet?

Answer

Convert 7 feet to inches by multiplying by 12: $7 \times 12 = 84$ inches.

The sidelength of a square is one-fourth its perimeter, so the sidelength here is one-fourth of 84 inches. This is $84 \div 4 = 21$ inches.

Square this to get the area:

$21 ^{2} = 21 \times 21 = 441$ square inches

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Question

The ratio of the length of a side of one square to the length of the side of another square is $\frac{a}{b}$ . Give the ratio of the area of the second square to the area of the first square.

Answer

The area of a square can be found as follows:

Where:

$x=Side\ Length$

So we can write:

$\frac{Area\ 2}{Area\ 1}=\frac{b^2}{a^2}$

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Question

What is the area of a square if the length of one side is $\sqrt{3}$ ?

Answer

The area of a square is found by multiplying one side by itself.

$A=s\times s=s^2$

We are given the side length, allowing us to solve.

$s=\sqrt{3}$

$A=(\sqrt{3})^2=3$

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Question

A square has an area of 36, and each side is equal to What is the value of ?

Answer

Each side of a square is equal to the square root of the area. The square root of 36 is 6, so each side is 6. Thus, 3x (being a side of the square is equal to 6. This means that x is equal to 2 because 3 times 2 is 6.

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Question

Find the area of a square with side length 10.

Answer

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

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Question

The area of a square is ?

Answer

The area of a square is the side length squared not the side length times .

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Question

If you are given one side length of a square, you can find the area with that information.

Answer

To find the area of a square, you multiple . But with a square all the sides are equal so the equation really is or the side length squared. Since you are given the side length, you can find the area.

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Question

A new building in New York City will have a footprint that is a perfect square, taking up a complete city block. If one city block is of a mile, what is the area taken up by the building?

Answer

A new building in New York City will have a footprint that is a perfect square, taking up a complete city block. If one city block is of a mile, what is the area taken up by the building?

Find the area of a square by raising the side length to the second power:

$A=s^2=\frac{1}{8}^2=\frac{1}{8}*\frac{1}{8}=\frac{1}{64}mi^2$

So our area is:

$\frac{1}{64}mi^2$

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Question

Use the following to answer the question.

Find the area of the square.

Answer

When finding the area of a square, we use the following formula:

$\text{area of square} = l \cdot w$

where l is the length and w is the width of the square.

Now, we know that a square has 4 equal sides. So given the square

we know the length is 6ft and the width is 6ft. So, we can substitute into the formula.

$\text{area of square} = 6\text{ft} \cdot 6\text{ft}$

$\text{area of square} = 36\text{ft}^2$

Note that the label is also squared. This is because when we multiply, we are also multiplying the label.

$\text{ft} \cdot \text{ft} = \text{ft}^2$

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Question

Find the area of a square with a width of 8 inches.

Answer

To find the perimeter of a square, we use the following formula:

$\text{area of square} = l \cdot w$

where _l_is the length and w is the width of the square.

Now, we know the width of the square is 8 inches. Because it is a square, we know that all sides are equal. Therefore, the length is also 8 inches. Knowing this, we can substitute into the formula. We get

$\text{area of square} = 8 \text{ inches} \cdot 8 \text{ inches}$

$\text{area of square} = 64 \text{ inches}^2$

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Question

You are playing Monopoly and notice that the dice is a cube. If the dice has a height of 2 centimeters, what is the area of one of its surfaces?

Answer

You are playing Monopoly and notice that the dice is a cube. If the dice has a height of 2 centimeters, what is the area of one of its surfaces?

We can begin by realizing that we need to find the area of just one surface of the cube. This surface will be a square, we know this because we are dealing with a cube.

So, we need to find the area of a square. Easy enough with the following formula:

$A_{square}=s^2$

Now, we just need to know "s." To find s, we need to look at the question. We are told that the height of the cube is 2cm. This means that the side length of our base (square) is also 2.

So...

$A_{square}=(2cm)^2=4cm^2$

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Question

Find the area of a square with a base of 9 inches.

Answer

To find the area of a square, we will use the following formula:

$\text{area of square} = l \cdot w$

where l is the length and _w_is the width of the square.

Now, we know the square has a base of length 9 inches. Because it is a square, we know that all sides are equal. This means all sides are 9 inches. Therefore, the width is also 9 inches. Knowing this, we can substitute into the formula. So,

$\text{area of square} = 9\text{in} \cdot 9\text{in}$

$\text{area of square} = 81\text{in}^2$

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Question

If you have a square deck, what is the area when one of the sides is feet?

Answer

The area of a square is the side length square, or multiplied by itself,

meaning your answer must be,

$A=10^{2}=100ft^2$ .

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Question

A square stamp has an edge length of 6 centimeters, what is its area?

Answer

A square stamp has an edge length of 6 centimeters, what is its area?

To find the area of a square, simply square the side length:

$A_{square}=s^2=(6cm)^2=36cm^2$

So our answer is

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Question

A city block is a perfect square with sides of $\frac{1}{2}mile$ .

What is the area of the city block?

Answer

A city block is a perfect square with sides of $\frac{1}{2}mile$ .

What is the area of the city block?

To find the area of a square, take the side length and square it.

$A_{square}=s^2=(\frac{1}{2}mi)^2=\frac{1}{2}mi*\frac{1}{2}mi=\frac{1}{4}mi^2$

So, we get:

$\frac{1}{4}mi^2$

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Question

Find the area of a square with a base of length 13 inches.

Answer

To find the area of a square, we will use the following formula:

$\text{area of square} = l \cdot w$

where l is the length and w is the width of the square.

Now, we know the base of the square has a length of 13 inches. Because it is a square, we know that all sides are equal. Therefore, the width is also 13 inches. Knowing this, we can substitute into the formula. We get

$\text{area of square} = 13\text{in} \cdot 13\text{in}$

$\text{area of square} = 169\text{in}^2$

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Question

Find the area of a square with a base of length 8 inches.

Answer

To find the area of a square, we will use the following formula:

$\text{area of square} = l \cdot w$

where l is the length and w is the width of the square.

Now, we know the base has a length of 8 inches. Because it is a square, we know that all sides are equal. Therefore, all sides have a length of 8 inches. This means the width is also 8 inches. Knowing this, we can substitute into the formula. We get

$\text{area of square} = 8\text{in} \cdot 8\text{in}$

$\text{area of square} = 64\text{in}^2$

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