Table of Contents
How do you find a missing area in a trapezoid?
Explanation: To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.
What is the area formula for a trapezoid if you break it up into two triangles?
The formula for the area of a trapezoid is A = ½(b1+b2)h, where b1 and b2 are the lengths of the bases and h is the height. If you only know the side lengths of a regular trapezoid, you can break the trapezoid into simple shapes to find the height and finish your calculation.
Why does the formula for the area of a trapezoid work?
The area of this parallelogram is its height (half-height of the trapezoid) times its base (sum of the bases of the trapezoid), so its area is half-height × (base1 + base2). Because the parallelogram is made from exactly the same “stuff” as the trapezoid, that’s the area of the trapezoid, too.
Why does the formula for area of a trapezoid work?
How do you derive the Forumula for the area of a trapezoid?
This page describes how to derive the forumula for the area of a trapezoid by creating a parallelogram from two congruent trapezoids. The formula is simply one half the area of this parallelogram. Start with a trapezoid with known base lengths (b1, b2) and altitude (height). Make a copy of it. Rotate the copy 180°.
What is the area of one of the two congruent trapezoids?
The parallelogram formed by the two congruent trapezoids has a base b 1 + b 2 and height h. Therefore, the area of this parallelogram is: A = (b 1 + b 2 )h. Since the parallelogram is made up of two congruent trapezoids, halving the above formula gives us the formula for the area of one of the trapezoids:
What is the result when two trapezoids are combined?
When the two trapezoids are combined in this way, the result is a parallelogram , which has two pairs of opposite, congruent sides. Recall that the area of a parallelogram is its altitude (h) times the length of either base.
How big is the base of the trapezoid?
The new trapezoid is upside down from how you usually see them, but don’t let that stop you! The short base b b is 21 inches long. The long base a a (this time at the top of the drawing) is 31 inches long. The altitude h h (no matter which way you look at the trapezoid) is 5 inches.