### All SSAT Middle Level Math Resources

## Example Questions

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

Steve's bedroom measures 20' by 18' by 8' high. He wants to paint the ceiling and all four walls using a paint that gets 360 square feet of coverage per gallon. A one-gallon can of the paint Steve wants costs $36.00; a one-quart can costs $13.00. What is the least amount of money that Steve can expect to spend on paint in order to paint his room?

**Possible Answers:**

**Correct answer:**

Two of the walls have area ; two have area ; the ceiling has area .

Therefore, the total area Steve wants to cover is

Divide 968 by 360 to get the number of gallons Steve needs to paint his bedroom:

Since , Steve needs to purchase either two gallon cans and three quart cans, or three gallon cans.

The first option will cost him ; the second option will cost him . The latter is the more economical option.

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

Give the area of the rectangle in the above diagram.

**Possible Answers:**

**Correct answer:**

The area of a rectangle is the product of its length and its height:

The rectangle has a perimeter of 80.64 square centimeters.

### Example Question #3 : How To Find The Area Of A Rectangle

Give the area of the rectangle in the above diagram.

**Possible Answers:**

**Correct answer:**

The area of a rectangle is the product of its length and its width:

The area of the rectangle is 42 square inches.

### Example Question #4 : How To Find The Area Of A Rectangle

Give the surface area of the above box in square centimeters.

**Possible Answers:**

**Correct answer:**

100 centimeters make one meter, so convert each of the dimensions of the box by multiplying by 100.

centimeters

centimeters

Use the surface area formula, substituting :

square centimeters

### Example Question #6 : Geometry

Above is a figure that comprises a red square and a white rectangle. The ratio of the length of the white rectangle to the sidelength of the square is . What percent of the entire figure is red?

**Possible Answers:**

**Correct answer:**

To make this easier, we will assume that the rectangle has length 5 and the square has sidelength 3. Then the area of the entire figure is

,

and the area of the square is

The square, therefore, takes up

of the entire figure.

### Example Question #5 : How To Find The Area Of A Rectangle

The rectangle above is inches long and inches wide. What is the area of the rectangle?

*Note: Figure not drawn to scale.*

**Possible Answers:**

**Correct answer:**

The area of the rectangle is . In order to find the area of a rectangle, multiply the length (5 inches) by the width (10 inches). The answer is in units^{2} because the area, by definition, is the number of square units that cover the inside of a figure.

### Example Question #2 : How To Find The Volume Of A Figure

The above depicts a rectangular swimming pool for an apartment. The pool is two meters deep everywhere. What is the volume of the pool in cubic meters?

**Possible Answers:**

The correct answer is not among the other choices.

**Correct answer:**

The pool can be seen as a rectangular prism with dimensions 24 meters by 15 meters by 2 meters; its volume is the product of these dimensions, or

cubic meters.

### Example Question #7 : Geometry

Note: Figure NOT drawn to scale.

What percent of the above figure is white?

**Possible Answers:**

**Correct answer:**

The large rectangle has length 80 and width 40, and, consequently, area

.

The white region is a rectangle with length 30 and width 20, and, consequently, area

.

The white region is

of the large rectangle.

### Example Question #6 : Geometry

What is the area of a rectangle with length and width ?

**Possible Answers:**

**Correct answer:**

The formula for the area, , of a rectangle when we are given its length, , and width, , is .

To calculate this area, just multiply the two terms.

### Example Question #1 : Rectangles

Order the following from least area to greatest area:

Figure A: A rectangle with length 10 inches and width 14 inches.

Figure B: A square with side length 1 foot.

Figure C: A triangle with base 16 inches and height 20 inches.

**Possible Answers:**

**Correct answer:**

Figure A has area square inches.

Figure B has area square inches, 1 foot being equal to 12 inches.

Figure C has area square inches.

The figures, arranged from least area to greatest, are A, B, C.

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