About the Trapezoid Angle Calculator

What is a Trapezoid?

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. In a trapezoid, we typically label the angles as A, B, C, and D, starting from the bottom left and moving clockwise.

How to Calculate Trapezoid Angles

To calculate the angles of a trapezoid, we use the following formula:

\[\tan A = \frac{2h}{a-b}\]

Where:

• A is the bottom angle
• h is the height of the trapezoid
• a is the length of the bottom base
• b is the length of the top base

Once we calculate angle A, we can find angle C (the top angle) by subtracting A from 180°:

\[C = 180° - A\]

In an isosceles trapezoid, the angles on each side are equal, so B = A and D = C.

Example Calculation

Let's calculate the angles for a trapezoid with bottom base a = 10, top base b = 6, and height h = 4:

1. Calculate angle A: \[\tan A = \frac{2h}{a-b} = \frac{2 \times 4}{10-6} = 2\] \[A = \arctan(2) \approx 63.4°\]
2. Calculate angle C: \[C = 180° - A = 180° - 63.4° \approx 116.6°\]

Therefore, the bottom angles (A and B) are approximately 63.4°, and the top angles (C and D) are approximately 116.6°.