# SSAT Middle Level Math : Geometry

## Example Questions

### Example Question #201 : Geometry

Measured in units, the bases of a trapezoid are  and , the lengths are , and the height is unknown.  What is the perimeter of the trapezoid in units?

Impossible to calculate.

Explanation:

The perimeter is solved by adding the two bases together,  and , along with both the lengths, .

Therefore the equation becomes,

### Example Question #11 : How To Find The Perimeter Of A Trapezoid

Measured in units, the bases of a trapezoid are  and , the lengths are , and the height is unknown.  What is the perimeter of the trapezoid in units?

Impossible to calculate

Explanation:

The perimeter is solved by adding the two bases together,  and , along with both the lengths, .

Therefore the equation becomes,

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

Find the perimeter of the trapezoid:

Explanation:

The perimeter of any shape is equal to the sum of the lengths of its sides:

### Example Question #11 : How To Find The Perimeter Of A Trapezoid

Find the perimeter of the given trapezoid if

Explanation:

In order to find the perimeter, we must find the sum of the outer edges:

Notice that we didn't use height in our calculation.

### Example Question #19 : How To Find The Perimeter Of A Trapezoid

Find the perimeter of the given trapezoid if

Explanation:

In order to find the perimeter, find the sum of the outer edges:

Notice that we didn't use height in our calculation.

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

The above diagram depicts a rectangle  with isosceles triangle .  is the midpoint of . What is the ratio of the area of the orange trapezoid to that of the white triangle?

Explanation:

We can simplify this problem by supposing that the length of one leg of a triangle is 2. Then the other leg is 2, and the area of the triangle is

Since  is the midpoint of  , . Also, since opposite sides of a rectangle are congruent,

.

This makes the trapezoid one with height 2 and bases 2 and 4, so

The ratio of the area of the trapezoid to that of the triangle is 6 to 2, which simplifies to 3 to 1.

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

Find the area of the trapezoid above.

Note: Image not drawn to scale.

Explanation:

The area of a trapezoid is equal to the average of the length of the two bases multiplied by the height.

The formula to find the area of a trapezoid is:

In this problem, the lengths of the bases are  and  Their average is . The height of the trapezoid is

Remember: the answer to the problem should have units in cm2 .

### Example Question #201 : Geometry

Find the area of a trapezoid with a height of  and base lengths of  and , respectively.

Explanation:

The area  of a trapezoid is equal to the average of its two bases ( and ) multiplied by its height . Therefore:

### Example Question #201 : Geometry

Find the area of a trapezoid with a height of  and base lengths of  and , respectively.

Explanation:

The area  of a trapezoid is equal to the average of its two bases ( and ) multiplied by its height . Therefore:

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

What is the area of the above trapezoid?