# SSAT Middle Level Math : Quadrilaterals

## Example Questions

### Example Question #31 : Quadrilaterals

The above figure shows the size and shape of a yard that is to be surrounded by some fence. How many feet of fence will be needed?

Note: all sides meet at right angles.

Explanation:

The best way to see that 750 feet of fence are needed is to look at this augmented diagram.

Note that two of the sides are extended to form a smaller rectangle whose sides can be deduced by subtraction. Since opposite sides of a rectangle are congruent, this allows us to fill in the two missing sidelengths of the original figure.

### Example Question #32 : Quadrilaterals

Give the perimeter of the rectangle in the above diagram.

Explanation:

The perimeter of a rectangle is the sum of the length and the width, multiplied by 2:

The rectangle has a perimeter of 38 centimeters.

### Example Question #33 : Quadrilaterals

Give the perimeter of the rectangle in the above diagram.

Explanation:

The perimeter of a rectangle can be calculated by multiplying two by the sum of the length and width of the rectangle.

The perimeter of the rectangle is  inches.

### Example Question #5 : How To Find The Perimeter Of A Rectangle

Figure NOT drawn to scale.

Give the perimeter of the green polygon in the above figure.

The perimeter cannot be determined from the information given.

Explanation:

Since opposite sides of a rectangle have the same measure, the missing sidelengths can be calculated as in the diagram below:

The sidelengths of the green polygon can now be added to find the perimeter:

### Example Question #34 : Quadrilaterals

The width of a rectangle is one-third of its length. If the width is given as  what is the perimeter of the rectangle in terms of ?

Explanation:

The perimeter of a rectangle is the sum of its sides.

The sum of the widths is  and since the width is one-third of the length, each length is . Since there are  lengths we get a total of . Widths + lengths =

### Example Question #35 : Quadrilaterals

You are given equilateral triangle  and Rectangle

with .

What is the perimeter of Rectangle  ?

Explanation:

is equilateral, so .

Also, since opposite sides of a rectangle are congruent,

and

The perimeter of Rectangle  is

### Example Question #36 : Quadrilaterals

A hectare is a unit of area equal to 10,000 square meters.

A 150-hectare plot of land is rectangular and is 1.2 kilometers in width. Give the perimeter of this land.

Explanation:

150 hectares is equal to  square meters.

The width of this land is 1.2 kilometers, or  meters. Divide the area by the width to get:

meters

The perimeter of the land is

meters, or  kilometers.

### Example Question #37 : Quadrilaterals

The length of a rectangle is two times as long as the width. The width is equal to  inches. What is the perimeter of the rectangle?

Explanation:

### Example Question #38 : Quadrilaterals

How many meters of fence are needed to enclose a rectangular field that has a length of 1000 meters and a width of 100 meters?

Explanation:

The perimeter of a rectangle is simply the sum of the four sides:

### Example Question #31 : Quadrilaterals

The perimeter of a rectangle with a length of  and a width of is . Find .

Explanation:

We know that:

where:

So we can write: