# ISEE Middle Level Math : Quadrilaterals

## Example Questions

### Example Question #61 : Squares

Find the area of a square with a width of 5in.

Explanation:

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

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

Now, we know the width of the square is 5in.  Because it is a square, all sides are equal.  Therefore, the length is also 5in.  So, we can substitute.  We get

### Example Question #62 : Squares

Find the area of a square with a length of 9in.

Explanation:

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

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

Now, we know the length of the square is 9in.  Because it is a square, all sides are equal.  Therefore, the width is also 9in.  So, we get

### Example Question #63 : Squares

Find the area of a square that has a width of 13in.

Explanation:

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

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

Now, we know the width of the square is 13in.  Because it is a square, all sides are equal.  Therefore, the length is also 13in.

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

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

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

Explanation:

The formula for the area, , of a rectangle when we are given its length, , and width, , is .

To calculate this area, just multiply the two terms.

### Example Question #321 : Ssat Middle Level Quantitative (Math)

Order the following from least area to greatest area:

Figure A: A rectangle with length 10 inches and width 14 inches.

Figure B: A square with side length 1 foot.

Figure C: A triangle with base 16 inches and height 20 inches.

Explanation:

Figure A has area  square inches.

Figure B has area  square inches, 1 foot being equal to 12 inches.

Figure C has area  square inches.

The figures, arranged from least area to greatest, are A, B, C.

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

Give the surface area of the above box in square inches.

Explanation:

Use the surface area formula, substituting  :

square inches

### Example Question #2 : Area Of A Rectangle Or Square

The area of the following rectangle is . Solve for .

Explanation:

The area of a rectangle can be found by multiplying the length by the width.

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

Give the area of the above rectangle in square feet.

Explanation:

Since 1 yard = 3 feet, multiply each dimension by 3 to convert from yards to feet:

Use the area formula, substituting :

square feet

### Example Question #61 : Quadrilaterals

The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?

Explanation:

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is , and its area is .

The perimeter of the first square is  , and its sidelength is . The area of this square is therefore .

The ratio of the areas is therefore .

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

The following question is about the Jones family wanting to buy square foot tiles for their rectangular basement. Their basement perimeter is 74 feet, with one of the sides being 15 feet long.

How many square foot titles are the Jones family needing to purchase in order to tile their basement?