Trigonometry Formulas for Area of Triangle
and Area of Parallelogram
The formula for the
area of a triangle is
where b stands for the base and h stands for the altitude
(height)
drawn to that base. 

(lettering the diagram is of no importance to the
formula) 
By using trigonometry in the right triangle (on the left
side of the diagram), we find:

Multiplying by b, gives .
Substituting this new value of h into the area formula gives the trig area of
triangle formula:


SAS Formula
for the area of a triangle
where the pattern is to use "two sides and
the sine of the included angle".

The diagonal of a parallelogram
divides the parallelogram into two congruent triangles.
Consequently, the area of a parallelogram can be thought of as
doubling the area of one of the triangles formed by a diagonal.
This gives the trig area formula for a
parallelogram:

Example 1:
Given the triangle at
the right, find its area, to the nearest hundredth.


Be careful!!! When using your graphing calculator, be
sure that you are in DEGREE Mode,
or that you are using the degree symbol
if in RADIAN Mode. 
Degree Mode: 


Radian Mode:
Find degree symbol under
ANGLE (2nd APPS) 



Example 2:
Given the parallelogram
at the right, find its area to the nearest hundredth.
Again!!! Be
sure that you are in DEGREE Mode,
or that you are using the degree symbol
if in RADIAN Mode. 
If this problem had asked for an
EXACT answer, do not
use your calculator, as the calculator rounds the value for sin
120º.
It will be necessary to use the 30º 60º 90º
reference triangle in Quadrant II. The EXACT ANSWER will
be
Check to see that the exact answer
yields the calculator decimal answer. 




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