# SSAT Middle Level Math : Geometry

## Example Questions

### Example Question #1 : How To Find A Square On A Coordinate Plane

A square has an area of  square units, what is the perimeter of the square?

Explanation:

In order to solve this problem, apply the formula , in order to conclude that the length of side  must equal  for the area to equal

Once you've found the length of side , apply the formula

### Example Question #31 : Coordinate Geometry

A square has an area of  square units. Find the perimeter.

Explanation:

In order to solve this problem, apply the formula , in order to conclude that the length of side  must equal  for the area to equal

Once you've found the length of side , apply the formula

### Example Question #1 : How To Find A Square On A Coordinate Plane

Find the area of the above square.

Explanation:

In order to find the area of the square above apply the formula: , where  the length of one side of the square.

Since
the solution is

### Example Question #1 : How To Find A Square On A Coordinate Plane

Find the area of the square shown above.

Explanation:

In order to find the area of the above square, apply the formula: , when  equals the length of one side of the square.

Since,  the solution is:

### Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

NOTE: Figure NOT drawn to scale.

What is the area of the parallelogram represented by the above figure?

Explanation:

The area of a parallelogram is its base multiplied by its height. The diagram below shows both in green:

### Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

Find the area of the above parallelogram given a height of 5 units, as shown to scale.

Explanation:

Since the diagram is drawn to scale, the base of the parallelogram must be 6 units in length. Using the area formula for a parallelogram:

### Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

Given a base of 12 units and an area of 120 square units, find the height of the paralellogram shown above.

Explanation:

The area formula for a parallelogram is:

Thus, to find the height, rearrange:

### Example Question #1 : How To Find A Parallelogram On A Coordinate Plane

The above parallelogram has an area of 30 square units. Which of the following could be the lengths of the base and height of this figure? (Image not drawn to scale.)

Explanation:

The formula for the area of a parallelogram is:

Thus, the base and height must equal 30 square units when multiplied together.

3 and 10 are the only combination of base and height which, when multiplied, equal the area of 30 square units.

### Example Question #1 : How To Find A Rectangle On A Coordinate Plane

In the above figure Dr. Robinson's shed is represented by the red square, and the shed has a perimeter of  yards. Find how much area Dr. Robinson has in his backyard--excluding the area that the shed occupies.

Explanation:

To find how much area Dr. Robinson has around his shed in his backyard, first apply the formula: , where  represents one side of the red shed. Given that
must equal  because .

Now you have enough information to find the area of the red shed.
Apply the formula:

Since the rectangular fence has a width of  yards and a length of  yards, apply the formula:  in order to find the area of the entire backyard.
Thus,

Then simply find the difference between the area of the entire yard and the area of the shed.

Thus the final solution is:

### Example Question #1 : How To Find A Rectangle On A Coordinate Plane

Identify the correct set of coordinates for rectangle .