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SAT Math : Plane Geometry

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Example Questions

Example Question #2 : Quadrilaterals

Find the perimeter of a parallelogram with one side equal to 6 and the other to 5.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter of a parallelogram. Thus,

P=2(s1+s2)=2*(5+6)=22

If you don't remember this formula, you can also just sum up all the sides of the parallelogram.

P=s1+s2+s3+s4

Where s1 and s3 are the long sides and s2 and s4 are the short sides. Since the two pairs of sides are equal, you can sub in the following.

s1=s3

s2=s4

A=s1+s1+s2+s2=2s1+2s2=2(s1+s2)

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

A contractor is going to re-tile a rectangular section of the kitchen floor. If the floor is 6ft x 3ft, and he is going to use square tiles with a side of 9in. How many tiles will be needed?

Possible Answers:

Correct answer:

Explanation:

We have to be careful of our units. The floor is given in feet and the tile in inches. Since the floor is 6ft x 3ft. we can say it is 72in x 36in, because 12 inches equals 1 foot. If the tiles are 9in x 9in we can fit 8 tiles along the length and 4 tiles along the width. To find the total number of tiles we multiply 8 x 4 = 32. Alternately we could find the area of the floor (72 x 36, and divide by the area of the tile 9 x 9)

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

The rectangular bathroom floor in Michael’s house is ten feet by twelve feet. He wants to purchase square tiles that are four inches long and four inches wide to cover the bathroom floor. If each square tile costs $2.50, how much money will Michael need to spend in order to purchase enough tiles to cover his entire bathroom floor?

Possible Answers:

$5400

$2700

$1920

$1080

$4800

Correct answer:

$2700

Explanation:

The dimensions for the bathroom are given in feet, but the dimensions of the tiles are given in inches; therefore, we need to convert the dimensions of the bathroom from feet to inches, because we can’t compare measurements easily unless we are using the same type of units.

Because there are twelve inches in a foot, we need to multiply the number of feet by twelve to convert from feet to inches.

10 feet = 10 x 12 inches = 120 inches

12 feet = 12 x 12 inches = 144 inches

This means that the bathroom floor is 120 inches by 144 inches. The area of Michael’s bathroom is therefore 120 x 144 in² = 17280 in².

Now, we need to find the area of the tiles in square inches and calculate how many tiles it would take to cover 17280 in².

Each tile is 4 in by 4 in, so the area of each tile is 4 x 4 in², or 16 in².

If there are 17280 in² to be covered, and each tile is 16 in², then the number of tiles we need is 17280 ÷ 16, which is 1080 tiles.

The question ultimately asks us for the cost of all these tiles; therefore, we need to multiply 1080 by 2.50, which is the price of each tile.

The total cost = 1080 x 2.50 dollars = 2700 dollars.

The answer is $2700.

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Example Question #1 : Quadrilaterals

Ron has a fixed length of wire that he uses to make a lot. On Monday, he uses the wire to make a rectangular lot. On Tuesday, he uses the same length of wire to form a square-shaped lot. Ron notices that the square lot has slightly more area, and he determines that the difference between the areas of the two lots is sixteen square units. What is the positive difference, in units, between the length and the width of the lot on Monday?

Possible Answers:

Correct answer:

Explanation:

Let’s say that the rectangular lot on Monday has a length of l and a width of w. The area of a rectangular is the product of the length and the width, so we can write the area of the lot on Monday as lw.

Next, we need to find an expression for the area of the lot on Tuesday. We are told that the lot is in the shape of a square and that it uses the same length of wire. If the length of the wire used is the same on both days, then the perimeter will have to remain the same. In other words, the perimeter of the square will equal the perimeter of the rectangle. The perimeter of a rectangle is given by 2l + 2w.

We also know that if s is the length of a side of a square, then the perimeter is 4s, because each side of the square is congruent. Let’s write an equation that sets the perimeter of the rectangle and the square equal.

2l + 2w = 4s

If we divide both sides by 4 and then simplify the expression, then we can write the length of the square as follows:

Recsquare1

Recsquare2

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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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SAT Math : Plane Geometry

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #2 : Quadrilaterals

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 : Quadrilaterals

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

All SAT Math Resources

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