Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 13: Triangles 179

altitude drawn from the opposite vertex, perpendicular to the base. This can sometimes cause
the altitude to fall outside the triangle. If that happens, extend the side to cross the altitude. The
length of the altitude is from the vertex to the point where it crosses the extension, but the length
of the base is only the part in the triangle. It doesn’t include the extension.

Suppose you want to find the area of an equilateral triangle with sides 12 inches long. You need
to find the length of an altitude, but if you remember the special right triangles, it’s not too bad.
The altitude in an equilateral triangle is also a median and an angle bisector, so it creates two
30 r-60r-90r triangles. The length of the altitude is half the length of a side times the square root
of three, so 63 inches. Use the side of 12 inches as the base and the 63 inches as the height.

The area of the triangle is approximately 62.35 square inches.

WORLDLY WISDOM

Area is always measured in square units: square inches, square feet, square

centimeters, etc. When you multiply feet times feet you get square feet. Meters

times meters yields square meters.

Tr ia n g le PQR has an area of 24 square centimeters. If the lengths of its sides are 3 centimeters,
6 centimeters, and 8 centimeters, find the length of the longest altitude.

The area of the triangle will be the same no matter which side is called the base, if the altitude is

drawn to that base. If we say the base is the 3 centimeter side, then A^1 bh
2

becomes 24 1

2

 3 h

and h = 16. If we use the 6 centimeter side as the base, then A^1 bh
2

becomes 24

1

2

 6 h and

h = 8. Declare that the base is the 8 centimeter side, then Abh
1
2
becomes 24 1
2

 8 h and h = 6.

The longest altitude is 16 cm.

A bh

A

A

1

2

1

2

12 6 3

36 3 62.35