The Home Plate Area Mystery

A major-league home plate. Dimensions in inches. From Math World. Click the image to go there.

The illustration shows the dimensions, in inches, of a major league home plate, according to the official rules of baseball.

What’s the area of the plate?

Another way to present this question is to note that major-league bases are 15 inches square—and wonder which is bigger.

In either case, the problem of figuring out the area of this pentagon involves taking shapes apart or sticking them together. This skill, of dissecting or composing shapes, is important for students; they need to visualize the easy shapes that are inside (or outside) the hard ones. It even appears in the core standards, obliquely, in 7.G.6. It’s also wonderful that there are different ways to do it.

In this case, it’s not too hard. Students who know how to find the area of a right triangle can be successful without much teacher intervention.

Most students cut off the top  8.5-by-17 rectangle and are left with a right triangle with a base and height of 12. Like this:

But if you encourage students to find another way, some might find one that involves subtraction rather than addition. If they can’t figure one out, you might read to them from the official rules of baseball:

1.05
Home base shall be marked by a five-sided slab of whitened rubber. It shall be a 17-inch square with two of the corners removed so that one edge is 17 inches long, two adjacent sides are 81/2 inches and the remaining two sides are 12 inches and set at an angle to make a point. It shall be set in the ground with the point at the intersection of the lines extending from home base to first base and to third base; with the 17-inch edge facing the pitcher’s plate, and the two 12-inch edges coinciding with the first and third base lines.

Oh! It’s a 17-inch square with the corners cut off! So it’s more like this:

 

The great thing that happens is that you get a different answer. Why? I won’t spoil it for you, but it’s a great question for slightly more experienced students.

(I came across this problem while preparing a content paper for a workshop for Fresno middle-school teachers. That paper appears on my resources page. Here is a direct link.)