# SSAT Middle Level Math : Geometry

## Example Questions

### Example Question #211 : Geometry

Find the area of the trapezoid:

Explanation:

The area of a trapezoid can be determined using the equation .

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

What is the area of the trapezoid?

Explanation:

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

### Example Question #213 : Geometry

The above diagram depicts a rectangle  with isosceles triangle . If  is the midpoint of , and the area of the orange region is , then what is the length of one leg of  ?

Explanation:

The length of a leg of  is equal to the height of the orange region, which is a trapezoid. Call this length/height .

Since the triangle is isosceles, then , and since  is the midpoint of , . Also, since opposite sides of a rectangle are congruent,

Therefore, the orange region is a trapezoid with bases  and  and height . Its area is 72, so we can set up and solve this equation using the area formula for a trapezoid:

This is the length of one leg of the triangle.

### Example Question #214 : Geometry

A trapezoid has a height of  inches and bases measuring  inches and  inches. What is its area?

Explanation:

Use the following formula, with :

### Example Question #2 : How To Find The Area Of A Trapezoid

What is the area of a trapezoid with height 20 inches and bases of length 100 and 200?

Explanation:

Set

The area of a trapezoid can be found using this formula:

The area is 3,000 square inches.

### Example Question #1 : Lines

Figure NOT drawn to scale.

Evaluate .

Explanation:

### Example Question #1 : How To Find Length Of A Line

A right triangle has one leg with a length of 6 feet and a hypotenuse of 10 feet. What is the length of the other leg?

Explanation:

In geometry, a right angle triangle can occur with the ratio of  in which 3 and 4 are each leg lengths, and 5 is the hypotenuse.

When you know the length of two sides of a right angle triangle like this, you can calculate the third side using this ratio.

Here, the ratio is:

This is double the   ratio. Therefore, we should multiply 4 by 2 in order to solve for the missing leg, which would be a value of 8 feet.

Another way to solve is to use the Pythagorean Theorem: .

We know that one leg is 6 feet and the hypotenuse is 10 feet.

### Example Question #171 : Plane Geometry

The radius of a circle is 6 inches. What is one-third of the diameter?

Explanation:

If the radius is equal to 6 inches, then the diameter will be double that value, or 12 inches. One-third of 12 is 4, which is therefore the correct answer.

### Example Question #219 : Geometry

A right triangle has one leg with length  and another leg with length . What is the length of the hypotenuse?

Explanation:

Since we are dealing with a right triangle, we can use the Pythagorean Theorem:

,

where  and  are leg lengths of  and , respectively, and  is the length of the hypotenuse.

Substituting values into the Theorem:

### Example Question #1 : How To Find Length Of A Line

Line  has a length of . It is bisected at point , and the resulting segment  is bisected again at point . What is the length of the line segment ?