7.4 Area of a Triangle
May 07, 2009
7-4 Area of a Triangle
1
A = 2 bh
Objectives:
Find the area of SAS triangles.
Find the area of SSS triangles.
May 3­5:09 PM
1
7.4 Area of a Triangle
May 07, 2009
Find the Area of SAS Triangles:
1
The formula A = 2 bh is useful when the base and height are given but what if you only know two sides and the included angle?
a
γ
h
sin γ = a
h
h = a sin γ
b
1
2
1
2
1
2
A = bh
a sin γ
A = b( )
A = absin γ
1
A = absin
γ
2
1
A = bcsin
α
2
1
2
A = acsin β
May 3­5:11 PM
2
7.4 Area of a Triangle
May 07, 2009
Example #1: Find the area of the triangle for which a = 8, b = 6, and γ = 30o. Round answers to two decimal places.
1
A = absin
γ
2
1
o
A = (8)(6)sin
30
2
2
A = 12 units
May 3­5:26 PM
3
7.4 Area of a Triangle
May 07, 2009
Find the Area of SSS Triangles:
1
The formula A = 2 bh is useful when the base and height are given but what if you only know all three sides and it is not a right triangle?
Use Heron's Formula...derived from the Law of Cosines.
Heron's Formula
A = √s(s ­ a)(s ­ b)(s ­ c)
1
where s = (a + b + c)
2
May 3­5:11 PM
4
7.4 Area of a Triangle
May 07, 2009
Example #2: Find the area of the triangle for which a = 4, b = 5, and c = 7. Round answers to two decimal places.
1
2
1
s = (4 + 5 + 7)
2
s = (a + b + c)
s = 8
A = √s(s ­ a)(s ­ b)(s ­ c)
A = √8(8 ­ 4)(8 ­ 5)(8 ­ 7)
A = √8(4)(3)(1)
A = 9.80 units2
May 3­5:26 PM
5
7.4 Area of a Triangle
May 07, 2009
Example #3: Find the area of the shaded region enclosed in a semicircle of diameter 8 centimeters. The length of the chord AB is 6 centimeters.
Hint: Triangle ABC is a right triangle.
B
6
A
8
C
Area of Semicircle
1
2
A = πr
2
1
2
A = π(4)
2
a2 + 62 = 82
a2 + 36 = 64
a2 = 28
a ≈ 5.29
Area of Triangle
1
A = (5.29)(6)
2
A = 15.87
Area of Shaded Region
A = 25.13 ­ 15.87
A = 9.26 cm2
A = 25.13
May 3­5:26 PM
6
7.4 Area of a Triangle
May 07, 2009
Homework:
p552 (6 - 24 even, 33, 35, 38, 40)
22
o
131
How would you find the area of this shape? 20
20
22
May 3­5:26 PM
7