Stadiums Calculator

What is a Stadium?

A stadium is a two-dimensional geometric shape consisting of a rectangle with semicircles at each end. It is also known as a discorectangle or obround.

Formulas for Stadiums

Let \(r\) be the radius of the semicircles, \(a\) be the length of the rectangle, \(P\) be the perimeter, and \(A\) be the area. Then:

1. Perimeter: \(P = 2\pi r + 2a\)
2. Area: \(A = \pi r^2 + 2ra\)

Step-by-Step Calculations

Let's calculate these properties for a stadium with radius \(r = 5\) units and rectangle length \(a = 10\) units:

1. Perimeter: \[P = 2\pi r + 2a = 2\pi \times 5 + 2 \times 10 = 31.42 + 20 = 51.42 \text{ units}\]
2. Area: \[A = \pi r^2 + 2ra = \pi \times 5^2 + 2 \times 5 \times 10 = 78.54 + 100 = 178.54 \text{ square units}\]

Visual Representation

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