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High School Math : How to find the area of a square

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Example Question #91 : Quadrilaterals

Square_with_diagonal

Find the area of a square with a diagonal of d=2.5cm .

Possible Answers:

$\dpi{100} 4.25cm^{2}$

Not enough information to solve

$6.25cm^{2}$

$5.0cm^{2}$

$3.125cm^{2}$

Correct answer:

$3.125cm^{2}$

Explanation:

A few facts need to be known to solve this problem. Observe that the diagonal of the square cuts it into two right isosceles triangles; therefore, the length of a side of the square to its diagonal is the same as an isosceles right triangle's leg to its hypotenuse: $1:\sqrt{2}$ .

$\frac{s}{d}=\frac{1}{\sqrt{2}}$

$\dpi{100} \frac{s}{2.5cm}=\frac{1}{\sqrt{2}}$

Rearrange an solve for .

$s=\frac{2.5cm}{\sqrt{2}}$

Now, solve for the area using the formula $A=s^{2}$ .

$A=(\frac{2.5cm}{\sqrt{2}})^{2}$

$\dpi{100} A=\frac{6.25cm^{2}}{2}$

$\rightarrow 3.125cm^{2}$

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Example Question #91 : Quadrilaterals

If the ratio of the sides of two squares is 2:1 , what is the ratio of the areas of those two squares?

Possible Answers:

8:1

2:1

4:1

6:1

Correct answer:

4:1

Explanation:

Express the ratio of the two sides of the squares as x:y = 2:1 . The area of each square is one side multiplied by itself, so the ratios of the areas would be x^2:y^2 = 2^2:1^2 . The right side of this equation simplifies to a ratio of 4:1 .

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Example Question #3 : Squares

If a completely fenced-in square-shaped yard requires 140 feet of fence, what is the area, in square feet, of the lot?

Possible Answers:

140

4900

1225

Correct answer:

1225

Explanation:

Since the yard is square in shape, we can divide the perimeter(140ft) by 4, giving us 35ft for each side. We then square 35 to give us the area, 1225 feet.

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Example Question #93 : Quadrilaterals

What is the area of a square with a diagonal of $5\sqrt{2}$ ?

Possible Answers:

100

$25\sqrt{2}$

Correct answer:

Explanation:

The formula for the area of a square is A=s*s . However, the problem gives us a diagonal and not a side.

Remember that all sides of a square are equal, so the diagonal cuts the square into two equal triangles, each a 45:45:90 right triangle.

If we use the Pythagorean Theorem, we see:

s^2+s^2=d^2

2s^2=d^2

Plug in our given diagonal to solve.

$2s^2=(5\sqrt{2})^2$

2s^2=50

s^2=25

$\sqrt{s^2}=\sqrt{25}$

s=5

From here we can plug our answer back into our original equation:

A=s*s

A=5*5

A=25

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Example Question #91 : Quadrilaterals

A half circle has an area of $18\pi$ . What is the area of a square with sides that measure the same length as the diameter of the half circle?

Possible Answers:

144

108

Correct answer:

144

Explanation:

If the area of the half circle is $18\pi$ , then the area of a full circle is twice that, or $36\pi$ .

Use the formula for the area of a circle to solve for the radius:

36π = πr²

r = 6

If the radius is 6, then the diameter is 12. We know that the sides of the square are the same length as the diameter, so each side has length 12.

Therefore the area of the square is 12 x 12 = 144.

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

Eric has 160 feet of fence for a parking lot he manages. If he is using all of the fencing, what is the area of the lot assuming it is square?

Possible Answers:

$80\ feet^{2}$

$16,000\ feet^{2}$

$160\ feet^{2}$

$1600\ feet^{2}$

$1200\ feet^{2}$

Correct answer:

$1600\ feet^{2}$

Explanation:

The area of a square is equal to its length times its width, so we need to figure out how long each side of the parking lot is. Since a square has four sides we calculate each side by dividing its perimeter by four.

$\frac{160}{4}=40$

Each side of the square lot will use 40 feet of fence.

$Area=length \times width$

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High School Math : How to find the area of a square

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #91 : Quadrilaterals

Example Question #91 : Quadrilaterals

Example Question #3 : Squares

Example Question #93 : Quadrilaterals

Example Question #91 : Quadrilaterals

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

All High School Math Resources

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