### All ISEE Middle Level Math Resources

## Example Questions

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

Which of the following is equal to the area of a square with perimeter 8 meters?

**Possible Answers:**

**Correct answer:**

The sidelength of a square is one-fourth its perimeter, so the sidelength here is one-fourth of 8, or 2, meters. One meter is equal to 100 centimeters, so the sidelength is 200 centimeters. Square this to get the area:

square centimeters.

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

Which of the following is the area of a square with perimeter 7 feet?

**Possible Answers:**

**Correct answer:**

Convert 7 feet to inches by multiplying by 12: inches.

The sidelength of a square is one-fourth its perimeter, so the sidelength here is one-fourth of 84 inches. This is inches.

Square this to get the area:

square inches

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

What is the area of a square with a side length of 4?

**Possible Answers:**

4

8

12

14

16

**Correct answer:**

16

The area of a square is represented by the equation .

Therefore the area of this square is .

### Example Question #31 : Geometry

Square A has sides measuring 5 meters. A second square, Square B, has sides that are 2 meters longer than the sides of Square A. What is the difference in area of Square A and Square B?

**Possible Answers:**

**Correct answer:**

The area of Square A is 5 * 5, or 25 m^{2}.

Since each of Square B's sides is 2 meters longer, the sides measure 7 meters. Therefore, the area of square B is 49 m^{2}.

Subtract to find the difference in areas:

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

The ratio of the length of a side of one square to the length of the side of another square is . Give the ratio of the area of the second square to the area of the first square.

**Possible Answers:**

**Correct answer:**

The area of a square can be found as follows:

Where:

So we can write:

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

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

**Possible Answers:**

**Correct answer:**

The area of a square is found by multiplying one side by itself.

We are given the side length, allowing us to solve.

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

A square has an area of 36, and each side is equal to What is the value of ?

**Possible Answers:**

**Correct answer:**

Each side of a square is equal to the square root of the area. The square root of 36 is 6, so each side is 6. Thus, 3x (being a side of the square is equal to 6. This means that x is equal to 2 because 3 times 2 is 6.

### Example Question #31 : Squares

Find the area of a square with side length 10.

**Possible Answers:**

**Correct answer:**

To find the area of a square, simply use the formula. Thus,

### Example Question #31 : Quadrilaterals

The area of a square is ?

**Possible Answers:**

**Correct answer:**

The area of a square is the side length squared not the side length times .

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

If you are given one side length of a square, you can find the area with that information.

**Possible Answers:**

False

True

**Correct answer:**

True

To find the area of a square, you multiple . But with a square all the sides are equal so the equation really is or the side length squared. Since you are given the side length, you can find the area.