### All ISEE Lower Level Quantitative Resources

## Example Questions

### Example Question #1 : Squares

What is the area of a square if one side of the square is 6?

**Possible Answers:**

**Correct answer:**

If one side of a square is 6, then each of the four sides of the square are equal to 6. To find the area of a square, we multiply the length and the height together. The length is 6, and the height is 6, thus the equation we use is .

Remember the formula for the area of a quadrilateral is . For a square, one side is equal to both the length and the width.

### Example Question #2 : Squares

One side of a square is centimeters long. What is the area of the square?

**Possible Answers:**

**Correct answer:**

The formula for finding the area of a square is , or, because this is a square, .

area = centimeters centimeters, or

### Example Question #51 : Plane Geometry

A right triangle has a base of and a height of .

What is the area of the rectangle made by 2 of these triangles aligned along the hypotenuse?

**Possible Answers:**

**Correct answer:**

If one combines the 2 identical triangles, their base and height become the length and width of the rectangle.

Area of a rectangle is:

In this case

### Example Question #4 : Squares

A square has an area of . What is the length of one side?

**Possible Answers:**

**Correct answer:**

You can find the area of a square by multiplying two sides together. All of the sides of a square are equal. In this case, , so the length of all of the sides of the square is 4 inches.

### Example Question #5 : Squares

Michaela drew th square below.

What is the area of the square?

**Possible Answers:**

12 square centimeters

100 square centimeters

112 square centimeters

48 square centimeters

144 square centimeters

**Correct answer:**

144 square centimeters

The area of a square can be found by multiplying the length of a side times itself. The side length of the above square is 12 cm. By finding 12 x 12, we find that the area of the square is 144 cm. squared.

### Example Question #6 : Squares

James found the area of the square below to be 36 centimeters squared.

What is the length of one side of the square?

**Possible Answers:**

8 centimeters

36 centimeters

6 centimeters

9 centimeters

18 centimeters

**Correct answer:**

6 centimeters

The area of a square can be found by multiplying the length of a side by itself. 36 is equal to 6 times 6, therefore the length of one side is 6 centimeters.

### Example Question #7 : Squares

Daphne found the area of the square below to be 81 centimeters squared.

What is the length of one side of the square?

**Possible Answers:**

81 centimeters

9 centimeters

8 centimeters

7 centimeters

20 centimeters

**Correct answer:**

9 centimeters

The area of a square can be found by multiplying the length of a side by itself. 81 is equal to 9 times 9, therefore the length of one side is 9 centimeters.

### Example Question #8 : Squares

If the area of a square is , what is the length of each side?

**Possible Answers:**

**Correct answer:**

To find the area of a square, the length must be multiplied by the height. Since a square has four equal sides, the length and width will have the same measurement. We must, therefore, find the square root of . Since , is the square root of , which makes it the measurement for both the length and the width of the square.