The Formula for the Area of a Trapezoid
The formula for the area of a trapezoid is a Grade 6 geometry skill in Reveal Math, Course 1. A trapezoid has two parallel sides called the bases (b1 and b2) and a perpendicular height h between them. The area formula is A = (1/2) x (b1 + b2) x h. This formula can be understood by observing that a trapezoid equals the average of its two bases multiplied by the height — or equivalently, two congruent trapezoids can be joined to form a parallelogram with base (b1 + b2) and height h. The formula is versatile because it also works for parallelograms (when b1 = b2) and triangles (when b1 = 0).
Key Concepts
Property Because of the visual tricks we learned, the area ($A$) of a trapezoid is half the height ($h$) multiplied by the sum of its two bases ($b 1$ and $b 2$). The formula is: $$A = \frac{1}{2}h(b 1 + b 2)$$.
Examples A trapezoid has a height of 8 inches and bases of 10 inches and 15 inches. Area = 1/2 x 8 x (10 + 15) = 4 x 25 = 100 square inches. A garden plot is shaped like a trapezoid with a height of 5 yards. The two parallel sides are 6 yards and 10 yards long. Area = 1/2 x 5 x (6 + 10) = 1/2 x 5 x 16 = 40 square yards.
Explanation Here is the step by step game plan: First, add the two parallel bases together (always do what's in the parentheses first!). Next, multiply that sum by the height. Finally, cut that number in half. It is a reliable recipe for success on every single problem!
Common Questions
What is the formula for the area of a trapezoid?
A = (1/2) x (b1 + b2) x h, where b1 and b2 are the two parallel bases and h is the perpendicular height. Add the bases, multiply by the height, then divide by 2.
Why is there a 1/2 in the trapezoid area formula?
Two congruent trapezoids placed together form a parallelogram with base (b1 + b2) and height h, giving area (b1 + b2) x h. Since each trapezoid is half the parallelogram, the trapezoid area is (1/2)(b1 + b2)h.
How do you identify the bases and height of a trapezoid?
The bases are the two parallel sides of the trapezoid (labeled b1 and b2). The height h is the perpendicular distance between the two bases — measured at a right angle. The slant legs are not the height.
Does the trapezoid formula work for special quadrilaterals?
Yes. When b1 = b2, the trapezoid is a parallelogram and the formula gives b x h. When b1 = 0, the shape is a triangle and the formula gives (1/2) x b x h. The trapezoid formula is the most general quadrilateral area formula.
What are common mistakes with the trapezoid area formula?
Using a leg length instead of the perpendicular height is the most common error. Also forgetting to add the two bases before multiplying (computing (1/2) x b1 x b2 x h is wrong).
When do students learn the trapezoid area formula?
The trapezoid area formula is introduced in Grade 6 in Reveal Math, Course 1, in the area of polygons unit.
Which textbook covers the formula for the area of a trapezoid?
Reveal Math, Course 1, used in Grade 6, covers the trapezoid area formula in the geometry and area chapter.