# SSAT Middle Level Math : How to find the area of a trapezoid

## Example Questions

### 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 #2 : 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 #3 : How To Find The Area Of A Trapezoid

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 #4 : How To Find The Area Of A Trapezoid

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 #3 : How To Find The Area Of A Trapezoid

What is the area of the above trapezoid?

Explanation:

To find the area of a trapezoid, multiply one half (or 0.5, since we are working with decimals) by the sum of the lengths of its bases (the parallel sides) by its height (the perpendicular distance between the bases). This quantity is

### Example Question #6 : How To Find The Area Of A Trapezoid

Find the area of the trapezoid:

Explanation:

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

### Example Question #3 : 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 #8 : How To Find The Area Of A Trapezoid

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 #261 : 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 #9 : 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.