# SSAT Middle Level Math : Geometry

## Example Questions

### Example Question #221 : Ssat Middle Level Quantitative (Math)

Dr. Robinson recently put a rectangular fence around his backyard. The fence has a width of  yards and a length of  yards. If Dr. Robinson paid  for every yard of fence, how much did the fence cost?

Explanation:

To find the cost of the fence, apply the formula  in order to first find the length of the perimeter of the fence.

Then multiply the perimeter by .

Thus, the solution is:

### Example Question #41 : Geometry

The rectangle shown above has a width of  and a length of . Find the area and perimeter of the rectangle.

Explanation:

To solve this problem apply the formulas:  &

Thus, the solution is:

### Example Question #221 : Ssat Middle Level Quantitative (Math)

A right triangle has legs 90 centimeters and 16 centimeters, What is its area?

Explanation:

The legs of a right triangle are its base and height, so use the area formula for a triangle with these dimension. Setting :

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

A triangle has base 18 inches and height 14 inches. What is its area?

Explanation:

Use the area formula for a triangle, setting :

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

What is the area of the above triangle?

Explanation:

The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:

That is, the area is 84 square inches.

### Example Question #4 : Plane Geometry

What is the area of the above triangle?

Explanation:

The two legs of a right triangle can serve as its base and its height. The area of the triangle is half the product of the two:

That is, the area is 3,000 square millimeters.

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

Note: Figure NOT drawn to scale.

The above triangle has an area of 450 square centimers. . What is  ?

Explanation:

The area of a triangle is one half the product of its base and its height - in the above diagram, that means

.

Substitute , and solve for  :

### Example Question #6 : Plane Geometry

Find the area of the triangle.

Note: Figure not drawn to scale.

Explanation:

To find the area of a triangle, multiply the base of the triangle by the height and then divide by two.

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

The quadrilateral in the above diagram is a square. What percent of it is white?

Explanation:

The area of the entire square is the square of the length of a side, or

.

The area of the white right triangle is half the product of its legs, or

.

Therefore, the area of that triangle is

of that of the entire square.

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

Mr. Jones owns the isosceles-triangle-shaped parcel of land seen in the above diagram. He sells the parcel represented in red to his brother. What is the area of the land he retains?

Explanation:

The area of a triangle is half the product of its base and its height, so Mr. Jones's parcel originally had area

square meters.

The portion he sold his brother, represented by the red right triangle, has area

square meters.

Therefore, the area of the parcel Mr. Jones retained is

square meters.