Time
for MATH MINUTE! (provide your favorite theme music here).
Get
out your paper & pencil because I have a new puzzle for you!!
PUZZLE #39 What is
the area? Oct.22-26
Can
you calculate the area of the following quadrilateral?
If so, what is it?
There
is more than one way to work this puzzle. First, try something, and then, if
you are stuck, see the following hint.
Hint: You may notice that this figure is the union of 2 right
triangles (triangles with a right angle), and we all remember that the area of
a right triangle is one-half the product of the length of the base times the
height, right?
If
you are really on your toes, you may also recall that some right triangles have
whole numbers for the lengths of their sides?
You
can check for this by using the Pythagorean equation: a2 + b2
= c2, where a & b are the lengths of the sides and c is the
length of the hypotenuse. If the equation holds, then the triangle is a right
triangle.
Like
a 3-4-5 triangle, which is a right triangle with sides of length 3, 4, and 5
units. This triangle is a right triangle, since 32 + 42 =
52 (check this).
Now,
you may wonder if there are any other right triangles with whole numbers for
the lengths of their sides, or you may actually know of some (good for you)?
So
what?
This
is the hidden part of the puzzle, can you figure it out?
Have
fun!
Send
your comments, ideas and solutions before Monday to this email address, and be sure to
put MM in the subject line: parksjm@potsdam.edu
Visit
us here online to see the results every Monday.
See
you next time on MATH MINUTE! (theme music fades out here).