Decagon Calculator

A regular decagon has ten equal sides, with interior angles of 144°.

How the Math Works

A regular decagon is a ten-sided polygon with all sides and angles equal. The area formula (10/4)·s²·cot(π/10) works by dividing the decagon into 10 identical isosceles triangles, each with a base equal to side length s. The cotangent function (cotangent = 1/tangent) accounts for the angle at the center of each triangle, which is 360°/10 = 36° or π/10 radians. Multiplying by s² and the constant factor gives the total area covered by all ten triangles combined.

Practical Applications

To use this calculator, simply enter the length of one side of your decagon in the input field. The calculator will automatically compute both the area and perimeter using the formula. You can apply this for architectural planning when designing decagonal structures, calculating material needs for decagonal tiles or decorative elements, or in geometry homework problems involving regular decagons. The results are precise and saved you from manual calculations that could lead to errors.

Day-to-Day Use

While decagonal shapes are less common than squares or circles, they appear in decorative architecture, art projects, certain coin designs, and ornamental garden layouts. Knowing how to calculate their area and perimeter helps you estimate materials for DIY decagon-shaped garden beds, determine fabric needs for decagonal tablecloths or banners, or understand the scale of architectural elements in buildings. This knowledge turns seemingly abstract geometry into practical problem-solving skills.

Worked example

Side 5 → area ≈ 192.36, perimeter 50.

FAQ