Area of a Triangle
7.3
JMerrill, 2009
Area of a Triangle
(Formula)




When the lengths of 2 sides of a
triangle and the measure of the
included angle are known, the triangle
is uniquely determined. Use:
S = ½ ab sin C
Do not memorize all the
individual formulas,
S = ½ bc sin A
memorize the pattern:
S = ½ ac sin B
S = ½ (one side)(2nd side)(sine of incl. angle)
Example



Two sides of a triangle have lengths
7cm and 4cm. The angle between the
sides measures 73o. Find the area of
the triangle.
S = ½ (7)(4)sin 73o
S = 13.388cm2
You Do #1


Given the triangle ABC with measures
of b = 3, c = 8, <A = 120o, find the
area:
10.392units2
Example

Find the area of a
regular hexagon
inscribed in a unit
circle (means the
radius is 1 unit).
Then approximate
the area to 3
significant digits.
Flashback to
geometry…what does
“regular” mean?
First, divide the
hexagon into six
congruent triangles.
Example


Second, label the
known quantities
S=6(½)(1)(1)sin60
Where did the 6
come from?

S=2.60 units2
1 60o 1
You Do #2

Find the area of a regular octagon
inscribed in a circle with a radius of
20. Round to the nearest tenth.
1131.4 units2
You Do: Challenge

Approximate the area
of the irregularlyshaped piece of land
16
(hint: split it into 2
triangles, one of which
110o
is a right triangle). All
measurements are
given in feet. Round to
12
the nearest whole
Area of right triangle: 30ft2
number.
Length of drawn segment: 13ft
Total area: 101ft2
5