Online Area of Trapezoid Calculator
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.
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.