Trapezoid Study Guide

Definition

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. The height of a trapezoid is the perpendicular distance between the bases.

Formulas

The area (A) of a trapezoid can be calculated using the formula:

A = (1/2) * h * (b1 + b2)

where h is the height of the trapezoid, and b1 and b2 are the lengths of the two parallel bases.

The perimeter (P) of a trapezoid can be calculated using the formula:

P = a + b1 + c + b2

where a, b1, c, and b2 are the lengths of the four sides of the trapezoid.

Properties

• A trapezoid has two pairs of base angles, where each pair adds up to 180 degrees.
• The diagonals of a trapezoid are not necessarily equal in length.
• The midsegment of a trapezoid, which connects the midpoints of the two non-parallel sides, is parallel to the bases and its length is the average of the lengths of the two bases.

Example Problem

Calculate the area of a trapezoid with a height of 8 units, a first base of length 5 units, and a second base of length 10 units.

A = (1/2) * 8 * (5 + 10) = 60 square units

Practice Problems

1. Find the perimeter of a trapezoid with side lengths 6, 8, 5, and 7 units.

2. Calculate the area of a trapezoid with a height of 12 units, a first base of length 9 units, and a second base of length 15 units.

3. Given a trapezoid with a first base of length 3 units, a second base of length 7 units, and a height of 4 units, find the length of the midsegment.