Datasheet

Area of a Triangle and Circular Sector Activity
Introduction
In this activity, you will learn how to calculate the area of a triangle and a circular
sector using trigonometry. The area of a triangle is defined to be one-half of the
product of the lengths of the two sides (a, b) and the sine of angle (C) included
between those two sides. The formula looks like:
a
area =
2
1
•a•b•sin C
C
b
Another useful formula for finding the area of a triangle is Heron’s formula In this
formula you need to know the length of the three sides (
a, b, c) to find the area of the
triangle. Heron’s formula is:
b

c
a

area =
))()(( csbsass −−− where s =
2
1
(a + b + c)
The area of a circular sector is defined to be one-half of the product of the radius ®
squared and the central angle. The formula is:
θ

r 
area =
2
1
• r
2
•
θ
or
θ

r 
Questions
1. Find the area of the following triangles for the given values using one of the
following formulas:
area =
2
1
•
a•b•sin C area =
2
1
•
a•c•sin B area =
2
1
•c•
b•sin A
a.
a = 5, b = 7, C = 35
o
area = __________
b.
b = 10, c = 8, A = 28
o
area = __________
 c. a = 16, c = 4, B = 40
o
area = __________
Activity 8 • Pre-Calculus with the Casio fx-9750GII