PSAT Math : Geometry

Study concepts, example questions & explanations for PSAT Math

varsity tutors app store varsity tutors android store

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:

10(x + 1)

5x + 10

6x2 + 5

5x + 5

6x2 + 10x

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

Example Question #3 : 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:

544

272

88

176

352

Correct answer:

176

Explanation:

Para-rec2

Para-rec3

Example Question #641 : 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:

Correct answer:

Explanation:

The area of the walls is given by

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

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

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:

\$120

\$225

\$310

\$280

\$350

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.

Example Question #61 : Quadrilaterals

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:

125\ ft^{2}

75\ ft^{2}

150\ 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}.

Example Question #21 : 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:

1536 ft2

768 ft2

1536 ft2

2464 ft2

192 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

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

Rectangle

Note: Figure NOT drawn to scale

What percent of Rectangle  is pink?

Possible Answers:

Correct answer:

Explanation:

The pink region is Rectangle . Its length and width are

so its area is the product of these, or

.

The length and width of Rectangle  are

so its area is the product of these, or

.

We want to know what percent 117 is of 240, which can be answered as follows:

Example Question #21 : Rectangles

Rectangle

Note: Figure NOT drawn to scale

Refer to the above diagram. 

40% of Rectangle  is pink.  .

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Rectangle  has length  and width , so it has area

.

300 is 40% of, or 0.40 times, the area of Rectangle , which we will call . We can determine  as follows:

.

The length of Rectangle  is

,

so its width is 

.

Since 

,

Example Question #661 : Geometry

Rectangle

Note: Figure NOT drawn to scale

What percent of Rectangle  is white?

Possible Answers:

Correct answer:

Explanation:

The pink region is Rectangle . Its length and width are

so its area is the product of these, or

.

The length and width of Rectangle  are

so its area is the product of these, or

.

The white region is Rectangle  cut from Rectangle , so its area is the difference of the two:

.

So we want to know what percent 162 is of 450, which can be answered as follows:

Example Question #662 : Geometry

Rectangle

Note: Figure NOT drawn to scale

Give the ratio of the perimeter of Rectangle  to that of Rectangle .

Possible Answers:

Correct answer:

Explanation:

The perimeter of Rectangle  is

Opposite sides of a rectangle are congruent, so 

and 

 

The perimeter of Rectangle  is 

Opposite sides of a rectangle are congruent, so

,

,

and

The ratio of the perimeters is

 - that is, 7 to 5.

Learning Tools by Varsity Tutors