Download 9.2 The Area of a Triangle

9.2 The Area of a Triangle DISCUSSION
Precalculus
When the lengths of 2 sides of a triangle and the measure of the angle between
them (the included angle) are known, the triangle is uniquely determined (there
can only be one triangle that will fit the description). In geometry, this is called
the side angle side theorem (SAS). We can determine the area of a triangle with
these conditions given, such as for the triangle shown below.
B
a
h
C
b
A
The general form used for the area of a triangle is _______________________.
In this case, we know the measure of angle C and the lengths b and a.
Using a trigonometric relationship, how can we find the value of h?
______________________________________________________
What will be the equation, then, for the area of the triangle?
______________________________________________________
In words, the formula for the area of a triangle is:
________________________________________________________________
Example 1. Two sides of a triangle have lengths 7 cm and 4 cm. The angle
between the sides measures 730. Find the area of the triangle.
Example 2. The area of ∆PQR is 15. If p = 5 and q = 10, find all possible
measures of  R.
Example 3. As shown in the diagram below,  C in ∆ABC is obtuse. Show
1
that the formula K = absin C gives the area K of ∆ABC.
2
B
h
a
b
C
A
Example 4. Find the area of the quadrilateral to the nearest square unit.
16
110°
5
90°
12
The Area of a Triangle Assignment
Precalculus
For problems 1 and 2, find the area of each ∆ABC.
1.) a.) a = 4, b = 5, C  30 0
b.) a = 4, b = 5, C  150 0
2.) a.) a = 10, b = 20, C  70 0
b.) a = 10, b = 20, C  110 0
3.) The area of ∆ABC is 15. If a = 12 and b = 5, find the possible measures of
C .
4.) The area of ∆PQR is 9. If q = 4 and r = 9, find the possible measures of
P .
5.) Adjacent sides of a parallelogram have lengths 6 cm and 7 cm, and the
measure of the included angle is 300. Find the area of the parallelogram.
6.) Find the area of the quadrilateral to the nearest square unit.
11
8
90°
115°
6