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2
C 14 in
2
D 14.5 in
Answer
Choice A is correct. The base has a length of 4 in., and the height has a length of 3.5 in., so the area is
.
If you answered C, you may have forgotten to multiply the product of the base and height by one-half. If
you answered D, you may have calculated the perimeter of the triangle.
Think about why the formula for area contains . We’ll address this in a later section.
Measuring Right Triangles: The Pythagorean Theorem
This is probably the most popular theorem in all of geometry. In fact, it’s pretty important algebraically, as
well.
The right triangle below has legs of length a and b, and a hypotenuse of length c.
Legs and Hypotenuse
The Pythagorean Theorem gives the relationship between the lengths of these sides. It says: The sum of
the squares of the lengths of the legs of a right triangle is equal to the square of the length of the
hypotenuse. (Note: This is only true for right triangles. If the lengths of the sides of any triangle satisfy the
Pythagorean Theorem, the triangle must be a right triangle.)
We can take “square” in its algebraic and its geometric senses. Algebraically, the Pythagorean Theorem
looks like this:
The theorem can also be interpreted in the geometric sense.
