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High School Math : Quadrilaterals

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

The length of a rectangular rug is five more than twice its width. The perimeter of the rug is 40 ft. What is the area of the rug?

Possible Answers:

$150\ ft^{2}$

$125\ ft^{2}$

$75\ ft^{2}$

$100\ ft^{2}$

$50\ ft^{2}$

Correct answer:

$75\ ft^{2}$

Explanation:

For a rectangle, $P=2w+2l$ and $A=lw$ where $w$ is the width and $l$ is the length.

Let $x=width$ and $2x+5=length$ .

So the equation to solve becomes $40=2x+2(2x+5)$ or $40=6x+10$ .

Thus $x=5\ ft$ and $2x+5=15\ ft$ , so the area is $75\ ft^{2}$ .

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

The length of a rectangle is 5 times its width. Its width is 3 inches long. What is the area of the rectangle in square inches?

Possible Answers:

Correct answer: 45

Explanation:

The length is 5 x 3 = 15 inches. Multiplied by the width of 3 inches, yields 45 in².

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

A rectangle’s base is twice its height. If the base is 8” long, what is the area of the rectangle?

Possible Answers:

24 in²

32 in²

64 in²

16 in²

12 in²

Correct answer:

32 in²

Explanation:

Rectangle

B = 2H

B = 8”

H = B/2 = 8/2 = 4”

Area = B x H = 8” X 4” = 32 in²

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

The length of a rectangle is two more than twice the width. The perimeter is 58ft. What is the area of the rectangle?

Possible Answers:

$168 \; ft^{2}$

$198 \; ft^{2}$

$154 \; ft^{2}$

$138 \; ft^{2}$

$180 \; ft^{2}$

Correct answer:

$180 \; ft^{2}$

Explanation:

For a rectangle, P = 2l + 2w and A = lw , where is the length and is the width.

Let be equal to the width. We know that the length is equal to "two more than twice with width."

l=2w+2

The equation to solve for the perimeter becomes 58 = 2(2w + 2) + 2w .

58 = 4w + 4+2w=6w+4

54=6w

9=w

Now that we know the width, we can solve for the length.

l=2w + 2 = 20

Now we can find the area using A = lw .

A=(20ft)(9ft)=180ft^2

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Example Question #11 : How To Find The Area Of A Rectangle

Rectangle

Find the area of a rectangle with a length of w=18in and a length of l=3.6ft .

Possible Answers:

$64.8ft^{2}$

$4.5ft^{2}$

$5.4 ft^{2}$

$4.64ft^{2}$

$6.44ft^{2}$

Correct answer:

$5.4 ft^{2}$

Explanation:

First, we need to convert the length and width of the rectangle into similiar units.

$w=\frac{18in}{1}*\frac{1ft}{12in}$

$\rightarrow 1.5ft$

Now, calculate the area.

A=l*w

A=3.6ft*1.5ft

$\rightarrow 5.4ft^{2}$

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Example Question #31 : Rectangles

Rectangle_with_diagonal

A rectangle has a diagonal of d=8cm and a width of w=5cm . What is the area of the rectangle?

Possible Answers:

$26.26cm^{2}$

Not enough information to solve

$40.00cm^{2}$

$22.31cm^{2}$

$\dpi{100} 31.22cm^{2}$

Correct answer:

$\dpi{100} 31.22cm^{2}$

Explanation:

We are given the rectangle's diagonal $\dpi{100} \dpi{100} (d=8cm)$ and width $\dpi{100} (w=5cm)$ and are asked to find its area. The diagonal forms two right triangles within the rectangle; therefore, we can use the Pythagorean theorem to find the length of the rectangle's missing side. Then we can use the formula A=l*w to find the are of the rectangle.

$a^{2}+b^{2}=c^{2}$

In our case, we can rename the variables to match our triangle.

$w^{2}+l^{2}=d^{2}$

$\dpi{100} \dpi{100} \dpi{100} (5cm)^{2}+l^{2}=(8cm)^{2}$

$\dpi{100} l^{2}=64cm^{2}-25cm^{2}$

$\dpi{100} \dpi{100} \dpi{100} \sqrt{l^{2}}=\sqrt{39cm^{2}}$

$\dpi{100} l=\sqrt{39cm^{2}}$

Now we can calculate the area.

$A=(\sqrt{39cm^{2}})*5cm$

$\rightarrow 31.22cm^{2}$

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Example Question #13 : How To Find The Area Of A Rectangle

Joe has a rectangluar yard and wants to fence in his yard as well as plant grass seed. His yard measures $100\; ft\times 75\; ft$ . The fence costs $\$1.50$ per foot, and the grass seed costs $\$0.75$ per square foot. How much money does he need to complete both projects?

Possible Answers:

$\$6,150$

$\$5,100$

$\$4,575$

$\$4,325$

$\$5,625$

Correct answer:

$\$6,150$

Explanation:

This problem requires you to find both the perimeter (fence) and the area (grass seed) of a rectangle where $l=100\; ft$ and $w=75\; ft$ .

Fence Problem (Perimeter):

$2(l+w)(1.50)= 2(100+75)(1.50) = \$525.00$

Grass Seed Problem (Area):

$(l\cdot w)(0.75)=(100\cdot 75)(0.75)= \$5,625.00$

So the total cost for both projects is $\$6,150$ .

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Example Question #14 : How To Find The Area Of A Rectangle

A rectangle has sides of 2x +1 units and units. If the perimeter of the rectangle is 104 units, what is its area?

Possible Answers:

728 units squared

209 units squared

units squared

154 units squared

315 units squared

Correct answer:

315 units squared

Explanation:

Since a rectangle has pairs of equal-length sides, multiplying each side by and adding the products together gives the perimeter of the rectangle. Use this fact to set up an equation with the given information about the rectangle's sides and perimeter. Solving for in this equation will provide necessary information for finding the rectangle's area:

2(2x+1) + 2(7) = 104

$\rightarrow 4x+2 + 14 = 104$

$\rightarrow 4x+ 16 = 104$

$\rightarrow 4x = 88$

$\rightarrow x = 22$

Multiplying the measure of the long side of the rectangle by the measure of the short side of the rectangle gives the rectangle's area. The length of the long side is given by substituting the solution for into the given expression 2x + 1 that defines its length. The short side is , giving the following equation to calculate the area:

$A = (2(22)+1) \times 7$

$\rightarrow A = 45 \times 7$

$\rightarrow A = 315$ units squared

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Example Question #31 : Rectangles

The ratio of the areas of two rectangles is 6:1 . If the larger rectangle has a length of and a width of , what is the area of the smaller rectangle?

Possible Answers:

units squared

Correct answer:

units squared

Explanation:

The area of the larger rectangle is calculated as $6\times 3 = 18$ units squared. Since the ratio of the larger to the smaller rectangle is 6:1 , dividing the larger rectangle's area by gives the area of the smaller rectangle:

$\frac{18}{6} = 3$ units squared

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Example Question #16 : How To Find The Area Of A Rectangle

Joey is working in his yard. In the middle of his $80\; ft\; by\; 40\; ft$ rectangular yard he places a round cement fountain. The fountain has a diameter of $18\; ft$ . One bag of grass seed covers 250 square feet. How many bags of grass seed will Joey need to cover his yard?

Possible Answers:

Correct answer:

Explanation:

First, find the area of the rectangular yard:

l*w=80*40=3200 square feet

Next, find the area of the round cement fountain:

$\pi r^{2}=\pi (9)^{2}\approx 3.14(9)^{2}\approx 254$ square feet

Then find the difference between the two:

3200-254=2946 square feet

Now, to get the number of grass seed bags needed, divide the area by 250 to get approximately 11.75 bags. Because one can't purchase a partial bag, the correct answer is the next largest whole number, or bags of grass seed.

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High School Math : Quadrilaterals

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

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

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

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

Example Question #11 : How To Find The Area Of A Rectangle

Example Question #31 : Rectangles

Example Question #13 : How To Find The Area Of A Rectangle

Example Question #14 : How To Find The Area Of A Rectangle

Example Question #31 : Rectangles

Example Question #16 : How To Find The Area Of A Rectangle

All High School Math Resources

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