GED Math - Area of a Quadrilateral

Find the area of a square with a side of .

Explanation

Write the formula for the area of a square.

Substitute the side.

The answer is:

If the area of square is $\text{in}^2$ , what is its perimeter?

$52;\textup{in}$

$13;\textup{in}$

$26;\textup{in}$

$40;\textup{in}$

$22;\textup{in}$

Explanation

Figuring out the perimeter of a square from this information is luckily pretty easy. Since the sides of a square are all the same size, you know also that .

Taking the square root of both sides, you get:

Now, the perimeter of the square is just $4 \cdot13$ , or $52;\textup{in}$ .

A rectangle has length 10 inches and width 5 inches. Each dimension is increased by 3 inches. By what percent has the area of the rectangle increased?

Explanation

The area of a rectangle is its length times its width.

Its original area is $10 \times 5 = 50$ square inches; its new area is $13 \times 8 = 104$ square inches. The area has increased by

$\frac{104 - 50}{50 } \times 100 = \frac{54}{50 } \times 100 = 108 %$ .

A square and a circle share a center as shown by the figure below.

If the length of a side of the square is and is half the length of the radius of the circle, to the nearest hundredths place, find the area of the shaded region.

Explanation

In order to find the area of the shaded region, we will need to find the area of the circle then subtract the area of the square from it.

Start by finding the area of the square. Since we know the side length of the square, we can write the following:

$\text{Area of Square}=4^2=16$

Next, we find the area of the circle. Since the question states that the length of a side of the square is half the radius of the circle, the radius of the circle must be . Thus, we can find the area of the circle.

$\text{Area of Circle}=\pi r^2=\pi(8)^2=64\pi$

Now, subtract these two values to find the area of the shaded region.

$\text{Area of Shaded Region}=64\pi-16=185.06$

If the perimeter of a square is $60;\textup{in}$ , what is its area?

$225;\textup{in}^2$

$30;\textup{in}^2$

$125;\textup{in}^2$

$205;\textup{in}^2$

$325;\textup{in}^2$

Explanation

Since the four sides of a square are equal, you know that the perimeter of a square is defined as:

For our data, this is:

Solving for , you get:

$\frac{60}{4}=\frac{4s}{4}$

Now, the area of a square is just:

or , which is the same as $225;\textup{in}^2$ .

A square has an area of $144\text{cm}^2$ . Find the length of one side.

$12\text{cm}$

$13\text{cm}$

$15\text{cm}$

$16\text{cm}$

$18\text{cm}$

Explanation

A square has 4 equal sides. The formula to find the area of a square is

where b is the length of one side of the square. To find the length of one side of the square, we will solve for b.

Now, we know the area of the square is $144\text{cm}^2$ . So, we will substitute and solve for b. So,

$144\text{cm}^2 = b^2$

$\sqrt{144\text{cm}^2} = \sqrt{b^2}$

$12\text{cm} = b$

$b = 12\text{cm}$

Therefore, the length of one side of the square is 12cm.

Teresa has a circular lot that has a diameter of feet. She wants to put in a square swimming pool. In square feet, what is the largest possible area that her swimming pool can be?

Explanation

In order to maximize the size of the swimming pool, the circular lot and the square pool must share the same center as shown by the figure below:

Now, notice that the diameter of the swimming pool is also the diagonal of the square.

We can then use the Pythagorean Theorem to find the length of a side of the square.

$125=\sqrt{\text{side}^2+\text{side}^2}$

Solve for the side length.

$125=\sqrt{2(\text{side})^2}$

$125=\text{side}(\sqrt{2})$

$\text{side}=\frac{125}{\sqrt{2}}=\frac{125\sqrt{2}}{2}$

Now, recall how to find the area of a square:

$\text{Area of Square}=(\text{side})^2$

Plug in the found length of the side to find the area.

$\text{Area}=(\frac{125\sqrt2}{2})^2=7812.5$

A square has an area of $196\text{cm}^2$ . Find the length of one side.

$14\text{cm}$

$13\text{cm}$

$15\text{cm}$

$16\text{cm}$

$18\text{cm}$

Explanation

A square has 4 equal sides. The formula to find the area of a square is

where b is the length of one side of the square. To find the length of one side of the square, we will solve for b.

Now, we know the area of the square is $196\text{cm}^2$ . So, we will substitute and solve for b. So,

$196\text{cm}^2 = b^2$

$\sqrt{196\text{cm}^2} = \sqrt{b^2}$

$14\text{cm} = b$

$b = 14\text{cm}$

Therefore, the length of one side of the square is 14cm.

Find the area of the trapezoid:

Question_10

Explanation

The area of a trapezoid is calculated using the following equation:

$A=\frac{b_1+b_2}{2}h=\frac{7+5}{2}(3)=\frac{12}{2}(3)=(6)(3)=18$

If a square has a length of 10in, find the area.

$100\text{in}^2$

$40\text{in}^2$

$50\text{in}^2$

$60\text{in}^2$

$125\text{in}^2$

Explanation

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

$A = l \cdot w$

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

Now, we know the length of the square is 10in. Because it is a square, all sides are equal. Therefore, the length is also 10in. So, we can substitute. We get

$A = 10\text{in} \cdot 10\text{in}$

$A = 100\text{in}^2$

Area of a Quadrilateral

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