## Monday, April 14, 2014

### Square, Rectangle, Parallelogram Problems, 8

Category: Plane Geometry

"Published in Vacaville, California, USA"

The official distance between home plate and second base in a baseball diamond is 120 ft. Find the area of the official ball diamond and the distances between the bases. (The official ball diamond is in the form of a square.)

Solution:

To illustrate the problem, it is better to post and label the picture as follows

 Photo by Math Principles in Everyday Life

In this problem, the diagonal of a square is given which is a distance between the home plate and the second base. Since the official ball diamond is a square, then the diagonal bisects the square of side x into two equal isosceles right triangles.

Let x = be the distances between the bases
d = be the distance between home plate and 2nd base
A = be the area of official ball diamond

Apply Pythagorean Theorem in order to solve for the distances between the bases as follows

or

Finally, the area of official ball diamond is