Trapezoid Calculator

What is a Trapezoid?

A trapezoid is a four-sided polygon (quadrilateral) with at least one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs.

Formulas for Trapezoids

Let \(b_A\) and \(b_B\) be the lengths of the bases, \(h\) be the height, and \(s_A\) and \(s_B\) be the lengths of the sides. Then:

1. Area: \(A = \frac{(b_A + b_B)}{2} \times h\)
2. Perimeter: \(P = b_A + b_B + s_A + s_B\)

Step-by-Step Calculations

Let's calculate these properties for a trapezoid with base A \(b_A = 8\) units, base B \(b_B = 5\) units, height \(h = 4\) units, side A \(s_A = 6\) units, and side B \(s_B = 7\) units:

1. Area: \[A = \frac{(b_A + b_B)}{2} \times h = \frac{(8 + 5)}{2} \times 4 = 26 \text{ square units}\]
2. Perimeter: \[P = b_A + b_B + s_A + s_B = 8 + 5 + 6 + 7 = 26 \text{ units}\]

Visual Representation

This diagram illustrates the trapezoid with the calculated dimensions and properties.