### All ISEE Lower Level Math Resources

## Example Questions

### Example Question #31 : Plane Geometry

If the length of a rectangle is 2r and the width of the rectangle is 3w, what is the area?

**Possible Answers:**

**Correct answer:**

The area of a rectangle is found by multiplying the length by the width. Given that the length is 2r and that the length is 3w, the area will be the product of those numbers, which is .

### Example Question #32 : Plane Geometry

A rectangle has a length of 10 feet and a width of 1 foot. What is the area of the rectangle?

**Possible Answers:**

**Correct answer:**

The area of a rectangle is calculated by multiplying the length by the width.

Given that the length is 10 feet and that the width is 1 foot we can multiply to find the final area:

### Example Question #33 : Plane Geometry

What is the area of a rectangle with a width of 6 inches and a length of 7 inches?

**Possible Answers:**

**Correct answer:**

The area of a rectangle is equal to the length multiplied by the width. Since the width is 6 inches and the length is 7 inches, the area is equal to 6 times 7.

The area is 42 square inches.

### Example Question #34 : Plane Geometry

If a rectangle has a perimeter of 40, a width of 4, and a length of 4x, what is the value of x?

**Possible Answers:**

**Correct answer:**

The perimeter of a rectangle is equal to .

Thus, .

Add like terms:

Subtract 8 from both sides:

Divide both sides by 8:

### Example Question #22 : How To Find The Area Of A Rectangle

A rectangle has a perimeter of 30. One of its sides has a length of 6. What is its area?

**Possible Answers:**

**Correct answer:**

If the rectangle has one side that is , we know that two of them must be that size. Therefore, we know that it looks something like this:

If the perimeter is 30, you know that the following equation holds:

This means that the other two sides can be found by solving for :

The area of a rectangle is equal to its base times its height:

### Example Question #35 : Plane Geometry

A rectangle has two sides that are each . Its other sides are twice this length. What is the area of the rectangle?

**Possible Answers:**

**Correct answer:**

If one side is , the doubled side must be . Therefore, the rectangle looks like this:

The area of a rectangle is equal to its base times its height:

### Example Question #36 : Plane Geometry

What is the area of the following rectangle?

**Possible Answers:**

**Correct answer:**

The area of a rectangle is defined as the base multiplied by its height. Therefore, for this rectangle:

### Example Question #25 : How To Find The Area Of A Rectangle

One side of a rectangle has a length of 10. What is the area of this rectangle if it has a perimeter of 120?

**Possible Answers:**

**Correct answer:**

Based on what we were told, our rectangle looks like this:

We know, therefore, that there is or remaining for the other two sides. This means that they are . So, our rectangle ultimately looks like this:

The area of a rectangle is its base times its height. Therefore, the area is:

### Example Question #26 : How To Find The Area Of A Rectangle

A rectangle has a width of and a length of . Find the area of the rectangle.

**Possible Answers:**

**Correct answer:**

To find the area of a rectangle apply the formula:

This problem provides the measurements for both the width and length of the rectangle.

Thus, the solution is:

### Example Question #27 : How To Find The Area Of A Rectangle

A rectangle has a width of and a perimeter measurement of . Find the area of the rectangle.

**Possible Answers:**

Not enough information is provided.

**Correct answer:**

In this problem you are given the width and perimeter of the rectangle. However, to solve for the area of the rectangle you must first find the length of the rectangle. To do so, work backwards using the formula:

Now that you know the width and length of the rectangle, apply the area formula:

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