Math Doubts

Area of a Running track

Formula

$A \,=\, 2lw+\pi(R^2-r^2)$

Introduction

The area of running track can be expressed in mathematical form and it can be used as a formula in mathematics to find the area of any running track field. It can be derived easily in mathematical form when you understand the geometrical science behind the construction of a running track.

area of running track field

Geometrically, the shape of a running track is the combination of both rectangle and annulus. So, you first have to learn how to find the area of a rectangle and the area of a circular ring.

running track with dimensions

Now, let’s denote the various dimensions of running track field algebraically as follows.

  1. Denote the length of straight track lane by a letter $l$.
  2. Represent the width of straight track lane by a letter $w$.
  3. Denote the radius of the outer circular lane by a letter $R$.
  4. Represent the radius of the inner circular lane by a letter $r$.
  5. Denote the area of running track by a letter $A$.

The area of a running track is equal to the sum of two times the area of rectangular lane and the area of annulus lane.

$A \,=\, 2lw+\pi(R^2-r^2)$

Proof

Learn how to derive a formula in algebraic form to find the area of a running track in mathematics.

Derivation
Problems

A worksheet of list of math questions on finding the areas of running track fields for your practice with solutions to learn how to find the area of any running track mathematically.

Worksheet