Lesson 7.1 Area of Triangles Notes
Trig/PCalc
Page 1 of 1
Areas of Triangles:
 Formula:
 Times when you don’t know the height, we
can still find the area of the triangle. (The
triangle will be either obtuse or acute.)
Using Trig, we can find the area of the
triangle…
o If you have two sides and the angle
between them (included angle).
o If you know the length of all three
sides.
Example 3: Find the area of the given triangle.
C
34.0 ft
5510'
B
42.0 ft
A
 Labeling the Triangle
A
B
Example 4: Heron of Alexandria, in the first
century AD, showed that if a triangle has sides of
length a, b, and c, then its area can be calculated
C
1
ab sin C
2
o Basically…Given the lengths of two
sides of a triangle and the included
angle, the area of the triangle is half
of the product of two sides and the
sine of the included angle.
 Area 
Example 1:
Find the area of triangle ABC:
A
11 cm
B
28
15 cm
Example 2: Find the area of triangle ABC if
A  2440', b  27.3 cm, c  11.7 cm .
C
using A  s  s  a  s  b  s  c  where
s
abc
.
2
a. Find the area of the right angled triangle
with sides 3 cm, 4 cm, and 5 cm:
i.
without using Heron’s formula.
ii.
using Heron’s formula.
b. Find the area of a triangle with sides of
length:
i.
6 cm, 8cm, and 12cm.
ii.
7.2 cm, 8.9 cm, and 9.7 cm.