Trapezoid Study Guide

Definition

A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid. The non-parallel sides are called the legs of the trapezoid.

Properties

• A trapezoid has four sides and four angles.
• The sum of the interior angles of a trapezoid is always 360 degrees.
• The lengths of the two parallel sides (bases) are different from each other.
• The diagonals of a trapezoid are not necessarily equal in length.

Formulas

Some important formulas related to trapezoids include:

• Area of a trapezoid: A = (1/2) * (b1 + b2) * h, where b1 and b2 are the lengths of the two bases, and h is the height of the trapezoid.
• Perimeter of a trapezoid: P = a + b1 + c + b2, where a, b1, c, and b2 are the lengths of the four sides of the trapezoid.

Example Problems

1. Calculate the area of a trapezoid with bases of length 6 cm and 10 cm, and a height of 8 cm.

2. Find the perimeter of a trapezoid with side lengths of 5 cm, 7 cm, 9 cm, and 6 cm.

Practice Questions

1. Find the area of a trapezoid with bases of length 12 cm and 16 cm, and a height of 10 cm.

2. Determine the perimeter of a trapezoid with side lengths of 8 cm, 6 cm, 12 cm, and 10 cm.