ACT Math - How to find the area of a square

Find the area of a square with side length 5.

Explanation

To solve, simply use the formula for the area of a square given side length s. Thus,

How much more area does a square with a side of 2r have than a circle with a radius r? Approximate π by using 22/7.

12/14 square units

1/7 square units

4/7 square units

6/7 square units

Explanation

The area of a circle is given by A = πr2 or 22/7r2

The area of a square is given by A = s2 or (2r)2 = 4r2

Then subtract the area of the circle from the area of the square and get 6/7 square units.

A square garden is inscribed inside a circular cobblestone path. If the radius of the cobblestone path is feet, what is the area of the garden?

Explanation

If a square is inscribed inside a circle, the diameter of the circle is the diagonal of the square. Since we know the radius of the circle is feet, the diameter must be feet. Thus, the diagonal of the square garden is feet.

All squares have congruent sides; thus, the diagonal of a square creates two isosceles right triangles. The ratio of the lengths of the sides of an isosceles right triangle are $x: x: x\sqrt2$ , where $x\sqrt2$ is the hypotenuse. Thus, to find the length of a side of a square from the diagonal, we must divide by $\sqrt2$ .

$s = \frac{90}{\sqrt2} = \frac{90\sqrt2}{2} = 45\sqrt2$

The area of a square is , so if one side is $45\sqrt2$ , our area is

$A = s^2 = (45\sqrt2)^2 = (2025\cdot 2) = 4050$

Thus, the area of our square garden is

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

140

1225

4900

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.

Find the area of a square whose side length is .

Explanation

To find area, simply square the side length. Thus,

The perimeter of a square is $\textup{in}$ . What is its area?

$\textup{in}^2$

$\textup{Not enough information provided}$

Explanation

The perimeter of a square is very easy to calculate. Since all of the sides are the same in length, it is merely:

From this, you can calculate the area merely by squaring the side's value:

$\textup{in}^2$

Square

A square is circumscribed on a circle with a 6 inch radius. What is the area of the square, in square inches?

144

$36\pi$

Explanation

We know that the radius of the circle is also half the length of the side of the square; therefore, we also know that the length of each side of the square is 12 inches.

Square

We need to square this number to find the area of the square.

What is the area of a square with a side length of $14\textup{yd}$ ?

$\textup{yd}^2$

Explanation

The area of a square is very easy. You merely need to square the length of any given side. That is, the area is defined as:

For our data, this is:

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?

$1600\ feet^{2}$

$80\ feet^{2}$

$160\ feet^{2}$

$16,000\ feet^{2}$

$1200\ feet^{2}$

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.

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