Let’s learn how to find the area of a trapezoid.
What is a Trapezoid?
A trapezoid is a 4-sided flat shape with one pair of parallel sides called its bases. The height (also called altitude) of a trapezoid is perpendicular to its bases. The other two non-parallel sides are called legs. Examples of trapezoid-shaped objects are flowerpots, handbags, pails, and other architectural things.
See the illustration of a trapezoid below.
How to Find the Area of a Trapezoid
The area of a 2-dimensional shape refers to the total amount of space enclosed within that shape. It is measured in cubic units, such as m2, cm2, km2, and in2. Make sure all units are the same before you compute.
Related Reading: Area of a Circle – Formula & Examples
To find the area of a trapezoid, multiply the average of the trapezoid’s two bases (parallel sides) and its height, as expressed in this formula:
A = (a + b) / 2 • h
Where:
A = Area of a trapezoid
a = the length of the trapezoid’s base 1
b = the length of the trapezoid’s base 2
h = height of the trapezoid
Example #1: Finding the Area of a Trapezoid when Given Measurements with the Same Units
Find the area of a trapezoid with the following measurements:
a = 10cm, b = 8cm, h = 6cm
Solution to Example #1:
Step 1. Write the given figures: a = 10cm, b = 8cm, h = 6cm.
Step 2. Plug the figures into the formula. Substitute 10cm for a, 8cm for b, and 6cm for h.
A = (a + b) / 2 • h
= (10cm + 8cm) / 2 • (6cm)
Step 3. Simplify.
A = 18cm / 2 • (6cm)
= 9cm • 6cm
A = 54cm2
Therefore, the area of the trapezoid is 54cm2.
Example #2: Finding the Area of a Trapezoid when Given Measurements with Different Units
Find the area of the trapezoid below.
Solution to Example #2:
Step 1. Write the given measurements: a = 5yd, b =126in, h = 4yd.
Step 2. Since all units must be the same, convert 126in into yards.
Recall: 1 yd = 36 in. Write the conversion as a fraction that equals to 1: (1yd / 36in) = 1.
126in • (1yd / 36in) = 126in • (1yd / 36in) = 126yd / 36 = 3.5yd
Therefore, the converted value of b is 3.5 yd.
Step 3. Plug the measurements into the formula. Substitute 5yd for a, 3.5yd for b, and 4yd for h.
A = (a + b) / 2 • h
= (5yd + 3.5yd) / 2 • (4yd)
Step 4. Simplify.
A = 8.5yd / 2 • (4yd)
= 4.25yd • 4yd
A = 17yd2
Therefore, the area of the trapezoid is 17yd2.
Example #3: Finding the Base of a Trapezoid
Find the other base of a trapezoid that has an area of 71.5cm2, height of 6.5cm, and base of 9cm.
Solution to Example #3:
Step 1. Write the formula for the area of a trapezoid: A = (a + b) / 2 • h OR A = (a + b)h / 2.
Use the latter to solve for the missing base.
Step 2. Let a be the missing base. Plug the given measurements into the formula.
Temporarily remove the units to avoid confusion.
A = (a + b)h / 2
71.5 = (a + 9) (6.5) / 2
Step 3. Simplify.
First, multiply 6.5cm by the expression (a + 9).
71.5 = (6.5a + 58.5) / 2
Multiply both sides of the equation by 2.
2 (71.5) = 2 [(6.5a + 58.5) / 2]
143 = 6.5a + 58.5
Subtract 58.5 from both sides.
143 – 58.5 = 6.5a + 58.5 – 58.5
85 = 6.5a
Divide both sides by 6.5.
85 / 6.5 = 6.5a / 6.5
13 = a
Therefore, the length of the other base is 13cm.
Checking the Solution to Example #3:
Plug the measurements into the formula for the area of trapezoid.
A = (a + b) h / 2
71.5cm2 = [(13cm + 9cm) (6.5cm)] /2
71.5cm2 = [(22cm) (6.5cm)] / 2
Simplify.
71.5cm2 = 143cm2 / 2
71.5cm2 = 71.5cm2
Thank you for reading. We hope it’s effective! Always feel free to revisit this page if you ever have any questions about the area of a trapezoid.
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