Name: ________________________
Date: ___________
AREA OF A TRIANGLE
INTRODUCTION TO COLLEGE MATH
bh 1
or b  h . This was only
2
2
useful if the height of the triangle was given to you. Using trigonometry, another formula for area can
be derived so that area can be found using 2 sides of the triangle and the included angle. This is what
we will focus on today.
In previous courses you have learned that the area of a triangle is A 
Area of a Triangle
1
A  ab sin C
2
Examples:
1. In the accompanying diagram of ABC below, AC  18 cm, BC  23 cm, and mC  50.
Find, to the nearest square centimeter, the area of ABC.
A
B
C
2. In ABC , a  12, b  18, and sin C  0.5. What is the number of square units in the area of ABC ?
3. In DEF , mD  71, mE  42, d  20, and e  16. Find, to the nearest tenth of a square unit, the
area of DEF.
4. In ABCD, AB  22.5 cm, BC  34.2 cm, and mB  56. Find, to the nearest tenth of a square
centimeter, the area of ABCD.
5. The cost per square inch to produce a sheet metal lid is $0.03. If a sheet metal lid is in the shape of
an equilateral triangle with each side measuring 20 inches, what is cost to produce it? Give your
answer to the nearest cent.
6. Matt wishes to enclose a garden in the shape of an equilateral triangle that has an area of 500
square feet. He expects to purchase fencing that costs $12.95 per linear foot in order to create the
enclosure. To the nearest dollar, what is the total cost of the fencing that Matt needs?
Mixed Review:
1. The period of the graph of the equation y  4 cos(2 x)  6 is
1
(1) 2
(2) 2
(3)

2
2. If sin   , and if  is in quadrant II, then the value of sin 2 is
3
4 5
4 5
3 7
(1) 
(2)
(3) 
9
9
13
(4) 
(4)
3 7
13
Name: ____________________________
Date: ___________
AREA OF A TRIANGLE
INTRODUCTION TO COLLEGE MATH- HOMEWORK
1. In ABC , a  14, b  5 and mC  30 . Which of the following is the area of ABC in square
units?
(1) 35
(2) 17.5
(3) 35 2
(3) 17 3
2. An angle of a parallelogram measures 100 . If the sides of the parallelogram measure 10 and 12,
then which of the following is the area of the parallelogram, accurate to the nearest tenth?
(1) 59.1
(2) 29.6
(3) 118.2
(4) 236.4
3. In triangle ABC the measure of side a is four times the measure of side b. If mC  150 , then
what is the area of ABC in terms of side b?
(1) b 2
(2)
1 2
b
4
(3)
1 2
b
8
(4)
1 2
b
2
4. The area of an equilateral triangle is 40 square units. What is the length of the side of the equilateral
triangle to the nearest hundredth?
5. In EFG , angle E is acute. If g = 12, f = 18 and the area of EFG = 95 square units, then find mE
to the nearest degree.
6. Jonah is creating a putting green in the shape of a parallelogram such that two sides of the
parallelogram measure 20 feet and 42 feet. The angle between the two sides measures 110 degrees. If
it costs $2.50 per square foot to lay down putting turf, how much will it cost to cover the entire
parallelogram?
7. Jenna wants to bird house with an opening in the shape of an equilateral triangle. If she wants the
triangle to have an overall area of 8 square inches, how long should each side of the equilateral triangle
be, to the nearest tenth of an inch?
8. An engineer wishes to design a truss system as comprised of two triangles as shown below. If all
lengths are in units of feet, what is the total area of the truss system to the nearest hundredth of a
square foot?
8.5
42
10.5
90
14.8