Area of a Trapezoid
In short: The area of a trapezoid is half the sum of its two parallel bases times its height, A = (1/2)(b1 + b2)h, found by averaging the bases and multiplying by the height.
6th GradeGeometry6.G.A.1
What is Area of a Trapezoid?
The area of a trapezoid uses the average of its two parallel sides. Place a second copy upside down beside the first and the pair forms a parallelogram whose base is \(b_1 + b_2\); one trapezoid is half of that.
Precisely, \(A = \frac{1}{2}(b_1 + b_2)h\), where \(b_1\) and \(b_2\) are the lengths of the parallel sides and \(h\) is the perpendicular distance between them. The two slanted legs are not used.
How to spot it
- A four-sided figure has exactly one pair of parallel sides, such as a ramp profile or a flowerbed.
- A diagram lists two different lengths on opposite sides and one perpendicular distance.
- A composite floor plan includes a slanted wall that turns a rectangle into a trapezoid.
- The question asks for a surface covered by a shape that narrows at one end.
The method
- Identify the two parallel sides and name their lengths \(b_1\) and \(b_2\).
- Add them, then multiply by the height.
- Halve the result, which is the same as using the average of the bases.
- State the area in square units.
Area of a Trapezoid: solved example
Problem
A trapezoid-shaped flowerbed at a park in Burlington has a short side of 5 meters, a long side of 9 meters, and a distance of 4 meters between them. How much ground does it cover?
Solution
Add the parallel sides: \(5 + 9 = 14\). Multiply by the height: \(14 \cdot 4 = 56\).
Halve: \(56 \div 2 = 28\). The bed covers 28 square meters.
Try it
Question 1
Find the area of a trapezoid with bases 7 cm and 13 cm and height 5 cm.
Show the answer
\(\frac{1}{2}(7 + 13)(5) = 10 \cdot 5 = 50\) square centimeters.
Question 2
A trapezoid has area 120 square feet, bases 8 and 12 feet. What is its height?
Show the answer
\(120 = \frac{1}{2}(20)h = 10h\), so \(h = 12\) feet.
Area of a Trapezoid vs. Area of a Parallelogram
A parallelogram has equal parallel sides, so the average of its bases is just the base and the formula reduces to \(bh\). A trapezoid has unequal parallel sides, so you must average the two before multiplying by the height.
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Whole dictionary: A–Z · 6th Grade · Geometry