# Advanced Geometry : How to find the area of a trapezoid

## Example Questions

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### Example Question #1 : Trapezoids

Which of the following shapes is a trapezoid?

Explanation:

A trapezoid is a four-sided shape with straight sides that has a pair of opposite parallel sides. The other sides may or may not be parallel. A square and a rectangle are both considered trapezoids.

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

What is the area of the following trapezoid?

Explanation:

The formula for the area of a trapezoid is:

,

where  is the value of the top base,  is value of the bottom base, and  is the value of the height.

Plugging in our values, we get:

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

What is the area of the trapezoid pictured above in square units?

Explanation:

The formula for the area of a trapezoid is the average of the bases times the height,

.

Looking at this problem and when the appropriate values are plugged in, the formula yields:

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

What is the height of the trapezoid pictured above?

Explanation:

To find the height, we must introduce two variables, , each representing the bases of the triangles on the outside, so that . (Equation 1)

The next step is to set up two Pythagorean Theorems,

(Equation 2, 3)

The next step is a substitution from the first equation,

(Equation 4)

and plugging it in to the second equation, yielding

(Equation 5)

The next step is to substitute from Equation 3 into equation 5,

which simplifies to

Once we have one of the bases, just plug into the Pythagorean Theorem,

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

A isosceles trapezoid with sides , and  has a height of , what is the area?

Explanation:

An isosceles trapezoid has two sides that are the same length and those are not the bases, so the bases are 10 and 20.

The area of the trapezoid then is:

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

If the height of a trapezoid is , bottom base is , and the top base is , what is the area?

Explanation:

The formula for finding the area of a trapezoid is:

Substitute the given values to find the area.

### Example Question #1 : Trapezoids

Find the area of a trapezoid with bases of length  and  and a height of .

Explanation:

The formula for the area of a trapezoid is:

Where  and  are the bases and  is the height. Using this formula and the given values, we get:

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

Find the area of a trapezoid with bases of  and  and a height of .

Explanation:

The formula for the area of a trapezoid is:

Where  and  are the bases and  is the height. Using this formula and the given values, we get:

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

Find the area of the above trapezoid.

Explanation:

The formula for the area of a trapezoid is:

Where  and  are the bases and  is the height. Using this formula and the given values, we get:

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

Find the area of the above trapezoid.