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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

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.

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.

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, \(b_2=\frac{2A}{h}-b_1\)

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.

**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.

Frequently Asked Questions

A trapezoid has exactly one pair of opposite sides that is parallel, but a parallelogram has both pairs of opposite sides parallel.

A trapezoid whose legs, that is, non-parallel sides, are congruent is called an isosceles trapezoid.

The area of a trapezoid is half of the height times the sum of its base lengths.

A trapezoid is a special case of a quadrilateral whose one pair of opposite sides is parallel.