# ISEE Upper Level Math : Rectangles

## Example Questions

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### Example Question #1 : Rectangles

A rectangle on the coordinate plane has its vertices at the points .

What percent of the rectangle is located in Quadrant I?

Explanation:

The total area of the rectangle is

.

The area of the portion of the rectangle in Quadrant I is

.

Therefore, the portion of the rectangle in Quadrant I is

.

### Example Question #2 : Rectangles

A rectangle and a square have the same perimeter. The area of the square is  square centimeters; the length of the rectangle is  centimeters. Give the width of the rectangle in centimeters.

Explanation:

The sidelength of a square with area  square centimeters is  centimeters; its perimeter, as well as that of the rectangle, is therefore  centimeters.

Using the formula for the perimeter of a rectangle, substitute  and solve for  as follows:

### Example Question #3 : Rectangles

In a rectangle, the width is  while the length is . If , what is the area of the rectangle?

Explanation:

In a rectangle in which the width is x while the length is 4x, the first step is to solve for x. If , the value of x can be found by dividing each side of this equation by 3.

Doing so gives us the information that x is equal to 3.

Thus, the area is equal to:

### Example Question #4 : Rectangles

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the area of your book cover?

Explanation:

Your geometry book has a rectangular front cover which is 12 inches by 8 inches.

What is the area of your book cover?

To find the area of a rectangle, use the following formula:

Plug in our knowns and solve:

### Example Question #5 : Rectangles

Find the area of a rectangle with a width of 5in and a length that is three times the width.

Explanation:

To find the area of a rectangle, we will use the following formula:

where l is the length and w is the width of the rectangle.

Now, we know the width of the rectangle is 5in.  We also know the length is three times the width.  Therefore, the length is 15in.

Knowing this, we can substitute into the formula.  We get

### Example Question #6 : Rectangles

Find the area of a rectangle with a width of 7cm and a length that is four times the width.

Explanation:

To find the area of a rectangle, we will use the following formula:

where l is the length and w is the width of the rectangle.

Now, we know the width of the rectangle is 7cm.  We also know the length is four times the width.  Therefore, the length is 28cm.

Knowing this, we will substitute into the formula.  We get

### Example Question #7 : Rectangles

Find the area of a rectangle with a width of 8cm and a length that is four times the width.

Explanation:

To find the area of a rectangle, we will use the following formula:

where l is the length and w is the width of the rectangle.

Now, we know the width of the rectangle is 8cm.  We also know the length of the rectangle is four times the width.  Therefore, the length of the rectangle is 32cm.

Knowing this, we will substitute into the formula.  We get

### Example Question #8 : Rectangles

You are designing a poster to put on the front of your refrigerator. If the refrigerator door is 2 feet wide by 4.5 feet tall, what is the area of the largest poster you could fit on the door?

Explanation:

You are designing a poster to put on the front of your refrigerator. If the refrigerator door is 2 feet wide by 4.5 feet tall, what is the area of the largest poster you could fit on the door?

We need to find the area of a shape. Given the context of a refrigerator door and a poster, we can assume that the poster will be a rectangle. To find the area of a rectangle, we need to multiply length and width.

### Example Question #9 : Rectangles

A rectangle has a width of 9cm and a length that is three times the width.  Find the area.

Explanation:

To find the area of a rectangle, we will use the following formula:

where l is the length and w is the width of the rectangle.

Now, we know the width of the rectangle is 9cm.  We also know the length of the rectangle is three times the width.  Therefore, the length is 27cm.  So, we can substitute.

### Example Question #10 : Rectangles

Find the area of a rectangle with a length of 12in and a width that is a third of the length.