### Area of a Trapezoid

#### Lesson Objective

In this lesson, we will learn about the area of a trapezoid.

#### About This Lesson

In this lesson, we will:

- In this lesson, we will learn about the area of a trapezoid.
- See an example on using the formula to find the trapezoid's area.
- See another example on using the formula to find the height of a trapezoid.

The study tips and math video below will explain more.

### Study Tips

#### Tip #1

A trapezoid has four sides where two sides are parallel to each other. The height of the trapezoid is perpendicular to the parallel sides. These are shown on the right.

Now, if a trapezoid has the height h and two parallel sides a and b, the area A, of the trapezoid will be:

The math video below will give more explanation on this. Also, we will see some examples on how to use this formula.

### Math Video

#### Lesson Video

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#### Math Video Transcript

00:00:03.150

In this lesson, we will learn about the area of a trapezoid.

00:00:08.030

First, let's consider this trapezoid with the height ‘h’, and two parallel sides, ‘a’ and ‘b’ respectively.

00:00:17.140

Now, to find the area of a trapezoid A, first we add ‘a' and 'b' together, and divide the added numbers with 2.

00:00:27.010

This gives (a+b)/2. Next, we multiply (a+b)/2, with the height of the trapezoid, ‘h’.

00:00:38.070

Hence, now we have the formula for the area of a trapezoid, A = ((a+b)/2)h.

00:00:47.240

Note that, it is very important to include the unit. Since this is the formula for area, its unit will be in the form of square unit.

00:00:57.020

We will see more explanations on this, in the upcoming example.

00:01:02.040

Now, let's see some examples on using this formula.

00:01:07.030

Find the area of this trapezoid when its height is 4cm, and the parallel sides are 5cm, and 9cm respectively.

00:01:17.080

First, we start with the formula for the area of a trapezoid, A = ((a+b)/2)h.

00:01:26.080

Since the shorter parallel side is given as 5cm, we can substitute ‘a’ with 5.

00:01:33.150

Similarly, since the longer parallel side is given as 9cm, we can substitute 'b' with 9.

00:01:41.230

Next, we can simplify by adding 5 with 9. This gives 14.

00:01:48.110

14 divided by 2, gives 7.

00:01:52.200

Now, since the height is given as 4cm, we can substitute 'h' with 4.

00:01:59.120

Multiplying 7 with 4, gives 28.

00:02:03.180

Note that, this number has no meaning unless we include the unit for it.

00:02:08.160

Since the sides of the trapezoid are in centimeter, the unit for the area will be in square

centimeter.
00:02:15.160

Hence, the area of this trapezoid is 28 square centimeter.

00:02:23.050

Next example, given that the area of this trapezoid is 9 square feet, and it parallel sides are 2ft, and 4ft respectively. Find its height.

00:02:34.200

Again, we start with the formula for the area of a trapezoid, A = ((a+b)/2)h.

00:02:44.040

Now, since the area, and the 2 parallel sides are given, we can find the height by solving this equation for h. Here's how.

00:02:53.240

Since the area is given as 9 square feet, we can substitute 'A' with 9,

00:03:00.100

Similarly, since the shorter parallel side is given as 2cm, we can substitute 'a' with 2.

00:03:08.100

Again, since the longer parallel side is given as 4cm, we can substitute 'b' with 4.

00:03:16.150

We can simplify this equation, by adding 2 with 4. This gives 6. 6 divided by 2, gives 3.

00:03:27.130

(3)h is the same as 3h.

00:03:32.010

Now, we have 3h equals to 9.

00:03:36.140

Let's rewrite this equation so that it will look neater.

00:03:40.190

To find 'h' we need to remove 3. We can do so by dividing both sides of the equation with 3.

00:03:49.040

By doing so, we have, ’h’ equals to 9 over 3.

00:03:54.170

9 divides by 3, gives 3.

00:03:58.190

Now, this number is meaningless unless we include the unit for it.

00:04:03.110

Since the parallel sides are given in feet, the height of the trapezoid will be in feet.

00:04:09.120

Therefore, the height of this trapezoid is 3ft.

00:04:15.010

That is all for this lesson. Try out the practice question to further your understanding.

### Practice Questions & More

#### Multiple Choice Questions (MCQ)

Now, let's try some MCQ questions to understand this lesson better.

You can start by going through the series of questions on the area of a trapezoid or pick your choice of question below.

- Question 1 on finding the area of a trapezoid
- Question 2 on finding the height of a trapezoid

#### Site-Search and Q&A Library

Please feel free to visit the Q&A Library. You can read the Q&As listed in any of the available categories such as Algebra, Graphs, Exponents and more. Also, you can submit math question, share or give comments there.