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High School Math : Plane Geometry

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Example Questions

Example Question #211 : Plane Geometry

George wants to paint the walls in his room blue. The ceilings are 10 ft tall and a carpet 12 ft by 15 ft covers the floor. One gallon of paint covers 400 $ft^{2}$ and costs $40. One quart of paint covers 100 $ft^{2}$ and costs $15. How much money will he spend on the blue paint?

Possible Answers:

$\$55$

$\$40$

$\$30$

$\$70$

$\$80$

Correct answer:

$\$70$

Explanation:

The area of the walls is given by $A = 2wh + 2lh = 2(12)(10) + 2(15)(10) = 540 ft^{2}$

One gallon of paint covers 400 $ft^{2}$ and the remaining 140 $ft^{2}$ would be covered by two quarts.

So one gallon and two quarts of paint would cost $\$40 + \$15 + \$15 = \$70$

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Example Question #184 : Plane Geometry

Daisy gets new carpet for her rectangluar room. Her floor is $21\ ft \times 24\ ft$ . The carpet sells for $5 per square yard. How much did she spend on her carpet?

Possible Answers:

$\$225$

$\$120$

$\$310$

$\$350$

$\$280$

Correct answer:

$\$280$

Explanation:

Since $3\ ft=1\ yd$ the room measurements are 7 yards by 8 yards. The area of the floor is thus 56 square yards. It would cost $5\cdot 56=\$280$ .

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Example Question #212 : Plane Geometry

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:

$150\ ft^{2}$

$100\ ft^{2}$

$75\ ft^{2}$

$125\ ft^{2}$

$50\ ft^{2}$

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 #213 : Plane Geometry

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

Possible Answers:

32 in²

16 in²

24 in²

12 in²

64 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 #214 : Plane Geometry

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:

$168 \; ft^{2}$

$138 \; ft^{2}$

$180 \; ft^{2}$

$198 \; ft^{2}$

$154 \; ft^{2}$

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 #215 : Plane Geometry

Rectangle

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

Possible Answers:

$6.44ft^{2}$

$64.8ft^{2}$

$4.5ft^{2}$

$5.4 ft^{2}$

$4.64ft^{2}$

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 #572 : High School Math

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:

$26.26cm^{2}$

$40.00cm^{2}$

$22.31cm^{2}$

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

Not enough information to solve

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 #573 : High School Math

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:

$\$4,325$

$\$5,100$

$\$5,625$

$\$6,150$

$\$4,575$

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 #31 : Rectangles

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

154 units squared

units squared

315 units squared

209 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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High School Math : Plane Geometry

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #211 : Plane Geometry

Example Question #184 : Plane Geometry

Example Question #212 : Plane Geometry

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

Example Question #213 : Plane Geometry

Example Question #214 : Plane Geometry

Example Question #215 : Plane Geometry

Example Question #572 : High School Math

Example Question #573 : High School Math

Example Question #31 : Rectangles

All High School Math Resources

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