Area of a trapezoid
The area of a trapezoid is found by multiplying the average of the two parallel bases by the height: A = 1/2(b1 + b2) x h. For a trapezoid with bases 8 cm and 12 cm and height 5 cm, the area is 1/2(8 + 12) x 5 = 50 square cm. This formula works because the trapezoid can be thought of as the average of two rectangles. Covered in Chapter 8 of Saxon Math Course 2, finding the area of a trapezoid is a key 7th grade geometry skill that builds on understanding of parallelogram and triangle areas.
Key Concepts
Property To find the area of a trapezoid, multiply the average of the bases by the height. The formula is: $$A = \frac{1}{2}(b 1 + b 2)h$$.
Examples A trapezoid has bases $b 1 = 8$ cm and $b 2 = 12$ cm, and height $h = 5$ cm. Area = $\frac{1}{2}(8 + 12) \times 5 = \frac{1}{2}(20) \times 5 = 50 \text{ cm}^2$. Find the area of a trapezoid with bases of 11 m and 15 m and a height of 8 m. Area = $\frac{1}{2}(11 + 15) \times 8 = \frac{1}{2}(26) \times 8 = 104 \text{ m}^2$.
Explanation A trapezoid has two different parallel sides, so which one do we use? Neither! The trick is to find the average of the two bases, then multiply that average by the height. This clever shortcut transforms the trapezoid into a simple rectangle with the same area, making the calculation super straightforward and avoiding any guesswork.
Common Questions
What is the formula for the area of a trapezoid?
A = 1/2(b1 + b2) x h, where b1 and b2 are the lengths of the two parallel bases and h is the perpendicular height between them.
How do you find the area of a trapezoid step by step?
Add the two bases, multiply by the height, then divide by 2. For bases 11 m and 15 m with height 8 m: (11 + 15) x 8 / 2 = 26 x 8 / 2 = 104 square meters.
Why do you average the two bases in the trapezoid area formula?
A trapezoid has two different-length parallel sides. Averaging them gives the equivalent width of a rectangle with the same area, making the calculation work.
What is the difference between the bases and the legs of a trapezoid?
The bases are the two parallel sides, and the legs are the two non-parallel sides. Only the bases and the perpendicular height are used in the area formula.
What are common mistakes when calculating trapezoid area?
Students often forget to divide by 2, or they use a leg length instead of the perpendicular height. Always ensure the height is measured at a 90-degree angle to the bases.
Is the area of a trapezoid part of 7th grade math?
Yes. Saxon Math Course 2 teaches the trapezoid area formula in Chapter 8, connecting it to prior work with parallelogram and triangle areas.