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SAT Math : Quadrilaterals

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Example Questions

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

A rectangle has a width of 2x. If the length is five more than 150% of the width, what is the area of the rectangle?

Possible Answers:

5x + 10

6x² + 10x

5x + 5

10(x + 1)

6x² + 5

Correct answer:

6x² + 10x

Explanation:

Given that w = 2x and l = 1.5w + 5, a substitution will show that l = 1.5(2x) + 5 = 3x + 5.

A = lw = (3x + 5)(2x) = 6x² + 10x

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

Para-rec1

Rectangle ABCD is shown in the figure above. Points A and B lie on the graph of y = 64 – x² , and points C and D lie on the graph of y = x² – 36. Segments AD and BC are both parallel to the y-axis. The x-coordinates of points A and B are equal to –k and k, respectively. If the value of k changes from 2 to 4, by how much will the area of rectangle ABCD increase?

Possible Answers:

272

176

544

352

Correct answer:

176

Explanation:

Para-rec2

Para-rec3

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

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:

$\$40$

$\$55$

$\$80$

$\$30$

$\$70$

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 #2 : 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:

$50\ ft^{2}$

$75\ ft^{2}$

$150\ ft^{2}$

$125\ ft^{2}$

$100\ ft^{2}$

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 front façade of a building is 100 feet tall and 40 feet wide. There are eight floors in the building, and each floor has four glass windows that are 8 feet wide and 6 feet tall along the front façade. What is the total area of the glass in the façade?

Possible Answers:

768 ft²

2464 ft²

1536 ft²

192 ft²

1536 ft²

Correct answer:

1536 ft²

Explanation:

Glass Area per Window = 8 ft x 6 ft = 48 ft²

Total Number of Windows = Windows per Floor * Number of Floors = 4 * 8 = 32 windows

Total Area of Glass = Area per Window * Total Number of Windows = 48 * 32 = 1536 ft²

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Example Question #41 : Rectangles

Two circles of a radius of {2}'' each sit inside a square with a side length of {8}'' . If the circles do not overlap, what is the area outside of the circles, but within the square?

Possible Answers:

$16+8\pi$

$36-6\pi$

$64-8\pi$

$36-8\pi$

$36-4\pi$

Correct answer:

$64-8\pi$

Explanation:

The area of a square = $\dpi{100} \small side^{2}$

The area of a circle is $\dpi{100} \small \pi r^{2}$

Area = Area of Square $\dpi{100} \small -$ 2(Area of Circle) =

$8^{2}-2\cdot \pi (2)^{2}$

$64-8\pi$

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Example Question #4 : New Sat Math No Calculator

The width of a rectangle is a+b . The length of the rectangle is . What must be the area?

Possible Answers:

a+bc

abc

ac+bc

ac+b

a+b+c

Correct answer:

ac+bc

Explanation:

The area of a rectangle is:

$A=\textup{Length}\times \textup{ Width}$

Substitute the variables into the formula.

A=(a+b)(c) = ac+bc

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Example Question #11 : Quadrilaterals

Find the area of a rectangle with side length 7 and 9.

Possible Answers:

$\frac{63}{2}$

Correct answer:

Explanation:

To solve, simply use the formula for the area of a rectangle.

Substitute in the side length of 7 and width of 9.

Thus,

A=w*l=7*9=63

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Example Question #192 : Sat Mathematics

Find the area of a rectanlge given width is 2 and length is 3.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the area of a rectangle. Thus,

A=w*l=2*3=6

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SAT Math : Quadrilaterals

Study concepts, example questions & explanations for SAT Math

All SAT 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 #184 : Plane Geometry

Example Question #2 : How To Find The Area Of A Rectangle

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

Example Question #41 : Rectangles

Example Question #4 : New Sat Math No Calculator

Example Question #11 : Quadrilaterals

Example Question #192 : Sat Mathematics

All SAT Math Resources

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