# PSAT Math : Geometry

## 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?

10(x + 1)

5x + 10

6x2 + 5

5x + 5

6x2 + 10x

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

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?

544

272

88

176

352

176

Explanation:

### 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 and costs $40. One quart of paint covers 100 and costs$15.  How much money will he spend on the blue paint?

Explanation:

The area of the walls is given by

One gallon of paint covers 400 and the remaining 140 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 .  The carpet sells for \$5 per square yard.  How much did she spend on her carpet?

Explanation:

Since  the room measurements are 7 yards by 8 yards.  The area of the floor is thus 56 square yards.  It would cost .

### 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?

Explanation:

For a rectangle, and  where  is the width and  is the length.

Let  and .

So the equation to solve becomes  or .

Thus  and , so the area is .

### 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?

1536 ft2

768 ft2

1536 ft2

2464 ft2

192 ft2

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

Note: Figure NOT drawn to scale

What percent of Rectangle  is pink?

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

Note: Figure NOT drawn to scale

Refer to the above diagram.

40% of Rectangle  is pink.  .

Evaluate .

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

Note: Figure NOT drawn to scale

What percent of Rectangle  is white?

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

Note: Figure NOT drawn to scale

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

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.