# SSAT Middle Level Math : Geometry

## Example Questions

### Example Question #1 : Plane Geometry

A triangle has sides  feet,  feet, and  feet. Calculate its perimeter.

Explanation:

The perimeter of any figure is the sum of the lengths of the sides: .

### Example Question #1 : Geometry

A right triangle with hypotenuse 65 has one leg of length 60. What is its perimeter?

Explanation:

By the Pythagorean Theorem, if  and  are the legs of a right triangle and  is its hypotenuse, then

.

Set  and solve for :

The perimeter of the triangle - the sum of the sidelengths - is

.

### Example Question #71 : Geometry

What is the perimeter of an equilateral triangle with a side length ?

Explanation:

The perimeter is equal to the sum of the length of the sides. An equilateral triangle has three sides with equal lengths.

### Example Question #3 : Plane Geometry

Find the perimeter of a triangle with sides , , and .

Explanation:

Perimeter involves adding up all of the sides of the shapes; in this case, it's a triangle. Perimeter equals . Therefore, the answer is .

### Example Question #4 : Plane Geometry

A right triangle has legs  feet and  feet long. What is its perimeter, in inches?

Explanation:

The length of the hypotenuse of the triangle can be found using the Pythagorean Theorem. Substitute :

feet

Its perimeter is  feet. Multiply by 12 to get the perimeter in inches:

inches

### Example Question #72 : Geometry

An equilateral triangle has perimeter  centimeters. How long is one side?

Explanation:

An equilateral triangle has three sides of equal measure, so divide its perimeter by :

### Example Question #31 : Triangles

Find the perimeter of an equilateral triangle with a base of 11in.

Explanation:

To find the perimeter of a triangle, we will use the following formula:

where a, b, and c are the lengths of the sides of the triangle.

Now, we know the base of the equilateral triangle is 11in.  Because it is an equilateral triangle, all sides are equal.  Therefore, all sides are 11in.

So, we can substitute.  We get

### Example Question #73 : Geometry

Which of these choices can the perimeter of an isosceles triangle possibly be if you know that two sides have lengths 12 and 13?

Explanation:

An isosceles triangle has two sides of equal length. If two sides of an isoscelese triangle are of length 12 and 13, then the third must be of length 12 or 13.

This makes the perimeter either

or

Of our choices, we choose 38.

### Example Question #74 : Geometry

Florence wants to build a fence to surround her square garden.  The garden has an area of 16 square yards. How much fencing will she need?

Explanation:

So this question requires you to know the formula for area for a square which is side squared.

Thus, , so one side is the square root of 16, or 4.

To figure out the perimeter, add up all of the sides of the square which are all the same (4).

### Example Question #75 : Geometry

A square has perimeter 89.4 centimeters. What is the length of one side?