8.1.4 – Areas of Non-Right
Triangles
• Using the idea behind the Law of Sines/Law of
Cosines (working with non-right triangles,
finding missing sides and or angles), we want
to extend the idea to finding other
information for non-right triangles
• One important one is the area of any triangle
General Area Formula
• Recall, the general area of a triangle is:
• (1/2) (base)(height)
• Another way to think of it is one-half the
product of the lengths of any two sides
Sine Formula
• Sine Formula Area:
• Area = (1/2)abSin(C)
• Area = (1/2)bcSin(A)
• Area = (1/2)acSin(B)
Heron’s Formula
• Alternatively, we can find the area without any
knowledge of angles
• Let s = (a+b+c)/2
• Then:
• Area =
s(s  a)( s  b)( s  c)
• Cannot use Heron’s Formula without
knowledge of all three sides
• If you know an angle, best to use the sine
formula
• Example. A person is considering purchasing a
triangular piece of property. The property is
enclosed by three roads. One road measures
147 feet, while a second measure 207 feet,
with an included angle of 72 degrees. What is
the area of the property?
• Example. Bob is building a pretty sail for his
boat. The bottom edge of the sail measures 7
feet, the vertical measures 11 feet, and the
diagonal measures 12 feet. How much fabric
does Bob need to create his sail?
• Example. A garden is formed between a trio of
sidewalks. One length of sidewalk measure 12
feet, while another measure 15 feet. If the
included angle is 100 degrees, find the area of
the enclosed garden.
• Assignment
• Pg. 615
• 88-92