# ISEE Lower Level Math : Geometry

## Example Questions

### Example Question #59 : How To Find The Area Of A Rectangle

Use the following rectangle to answer the question:

Find the area.

Explanation:

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

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

So, given the rectangle

we can see the length is 11in and the width is 5in.

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

### Example Question #60 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a width of 3cm 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 3cm.  We also know the length is four times the width.  Therefore, the length is 12cm.

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

### Example Question #61 : How To Find The Area Of A Rectangle

Find the area of a rectangle with a length of 16in and a width that is half the length.

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 length of the rectangle is 16in.  We also know the width is half of the length.  Therefore, the width is 8in.

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

### Example Question #61 : Rectangles

Find the area of the following rectangle:

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, given the rectangle

we can see the length is 11in and the width is 5in.  Knowing this, we can substitute into the formula.  We get

### Example Question #1022 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Find the area of a rectangle with a width of 4in and a length that is two 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 4in.  We also know the length of the rectangle is two times the width.  Therefore, the length is 8in.  So, we get

### Example Question #91 : Geometry

Dennis is building a fence around his field to keep his cattle from getting off the property. If Dennis’ field is  miles long and  miles wide, how much fence will Dennis need to surround all of his property?

Explanation:

In order to determine how much fence Dennis will need, we must find the perimeter of his property, which can be found using the formula . When we plug  in the  and  in for , we find that Dennis needs  of fence to surround his property.

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

Give the perimeter of the rectangle in the above diagram.

Explanation:

Add the length and the height, then multiply the sum by two:

The rectangle has a perimeter of 58 inches.

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

Give the perimeter of the above rectangle in feet.

Explanation:

Use the following formula, substituting  :

Now, divide this by 12 to convert inches to feet.

6 inches make half of a foot, so this means the perimeter is  feet.

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

What is the perimeter of a rectangle that has a length of  inches and a width of  inches?

Explanation:

The perimeter of a shape is the sum of all its sides. To find the perimeter of a rectangle, one can use the formula listed above, , since a rectangle has opposite sides of equal length.

The length of the rectangle is :

The width of the rectangle is :

.

Therefore, the perimeter is .

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

What is the perimeter of a rectangle with length equal to 5 and width equal to 3?

8

16

15

30