Area of Trapezoid Calculator | Free Online Area of Trapezoid Calculator with Steps - BYJUS

# Area of Trapezoid Calculator

The area of a trapezoid calculator is a free online tool that helps us calculate the area of trapezoid, as well as its base length and height. Let us familiarize ourselves with the calculator....Read MoreRead Less

### How to use the ‘Area of Trapezoid Calculator’?

Follow the steps below to use the area of trapezoid calculator:

Step 1: Enter the three known measures (from base lengths, height and area) into the respective input boxes and the unknown measure will be calculated.

Step 2: Select the appropriate units for the input and output.

Step 4: Click on the ‘Solve’ button to obtain the result.

Step 5: Click on the ‘Show Steps’ button to know the steps that lead to the solution to find the missing measure.

Step 6: Click on the   button to enter new inputs and start over.

Step 7: Click on the ‘Example’ button to play with different random input values.

Step 8: Click on the ‘Explore’ button to visualize the relation between the area of trapezoid and the area of a parallelogram.

Step 9: When on the ‘Explore’ page, click the ‘Calculate’ button if you want to go back to the calculator.

### What is a Trapezoid?

A trapezoid is a quadrilateral that has exactly one pair of opposite sides that are parallel. The parallel sides are known as bases of the trapezoid, and the non-parallel sides are called its legs. The perpendicular distance between the bases is called the height.

### Formulas used in the ‘Area of Trapezoid Calculator’

Consider a trapezoid with base lengths $$b_1$$ and $$b_2$$ and height h

The area of the trapezoid, A = $$\frac{1}{2}\times h \times (b_1+b_2)$$

On rearranging the formula, we get,

• Height of trapezoid, h = $$\frac{2A}{(b_1+b_2)}$$

• Base length, $$b_1=\frac{2A}{h}-b_2$$

• Base length, $$b_2=\frac{2A}{h}-b_1$$

### Relationship Between the Area of a Trapezoid and the Area of a Parallelogram

Let us consider a trapezoid with base lengths x and y and height h.

Area of trapezoid, A = $$\frac{1}{2} \times h \times (x+y)$$

Now take another trapezoid such that it is congruent to the above  trapezoid. Let’s join these trapezoids along the leg of the first trapezoid, such that a parallelogram of base (x + y) and height h is formed as shown below.

So, the area of the parallelogram = 2 $$\times$$ Area of the trapezoid

= $$2 \times \frac{1}{2} \times h \times (x+y)$$

= (x + y) $$\times$$ h

Also we know that, area of parallelogram = base $$\times$$ height

= (x + y) $$\times$$ h

From the above observation, we can conclude that the area of a parallelogram formed by joining two congruent trapezoids along one of its legs is double the area of the trapezoid.

### Solved Examples

Example 1: Find the area of the trapezoid shown in the image.

Solution:

Area of trapezoid, A = $$\frac{1}{2} \times h \times (b_1+b_2)$$

= $$\frac{1}{2} \times 3 \times (4+5)$$

= 13.5 square feet

So, the area of the trapezoid is 13.5 square feet.

Example 2: Find the height of the given trapezoid.

Solution:

Area of trapezoid, A = $$\frac{1}{2} \times h \times (b_1+b_2)$$

Rearrange the formula, to find h.

Therefore, h = $$\frac{2A}{(b_1+b_2)}$$

h = $$\frac{2 \times 68}{(12+15)}$$

h = $$\frac{136}{27}$$

h = 5.037 centimeters

So, the height of the given trapezoid is 5.037 centimeters.

Example 3: Find the missing base length of the trapezoid.

Solution:

A = $$\frac{1}{2} \times h \times (b_1+b_2)$$

Rearrange the formula, to find $$b_1$$.

Therefore, $$b_1=\frac{2A}{h}-b_1$$

$$b_1=\frac{2 \times 24}{4}-8$$

$$b_1$$ = 12 – 8

$$b_1$$ = 4 inches

So, the required base length is 4 inches.