The figure shows an aerial view of a playground. If David runs around the field three times, he covers a distance of yards.

Answer 1

He runs a distance = 3 times the perimeter of the field.

If the field is rectangular shaped, he runs 3(2L +2W) = 6L +6W where L=length and W= Width

if the field is square shaped, he runs 3(4s) = 12s where s= a side of the square

if the field is an equilateral triangular shaped he runs 3(3s) = 9s where s= a side of the triangle

if the field is circular, then he runs 3 times the circumference of the field = 3pi(r^2) where r= the radius of the circle and pi= about 3.14159. 3pi(r^2) = about 3(3.14159)r^2 = 9.42477r^2 = about 9.4r^2 = 9.4(d/2)^2 - (9.4/4)d^2 = about 2.4d^2 where d= diameter

whatever the polygon shape, add up each side then multiply that sum by 3 to get how far he runs

if the field is polygon shaped, with n equal sides, he runs 3ns where n= number of sides and s= length of a side

many tracks have a track that is rectangular shaped, but with semi-circular areas at both ends, similar to most football fields. then the perimeter = 2L + piW, multiply that by 3 to get how far he ran. but not really, as it's more of an elliptical oval , like a 2 dimensional egg shape, around the football field. then calculate the perimeter of the ellipse, then multiply by 3