## Wednesday, April 23, 2014

### Circle - Rectangle Problems

Category: Plane Geometry

"Published in Newark, California, USA"

The quarter mile race track shown in the figure has parallel sides AB and CD, each 315 ft. long. If the ends are semicircles, find the area bounded by the track. If a race is run from S to D by way of C, find the length of the race in yards, given that arc SC = 44/67 x arc AC. (1 mile = 5280 ft.)

 Photo by Math Principles in Everyday Life

Solution:

The quarter mile race track consists of  two semicircles and a rectangle. Let's divide the given figure as follows

 Photo by Math Principles in Everyday Life

Let T = be the total distance of a race which is equal to 0.25 miles
d = be the diameter of the semicircles
C = circumference of a circle which is equal to the total  length of two arcs of semicircles
A = total area of a quarter mile race track

The total distance of a race in feet is equal to

The total distance of a race is

The total length of the two semicircles is equal to the circumference of a circle because the diameter of the two semicircles is the same which is d. The diameter of the two semicircles or the width of a rectangle is equal to

The total area of a quarter mile race is

The length of a race from S to D by way of C in feet is equal to

The length of a race from S to D by way of C in yards is equal to