Triangles;
Objective: To find the
perimeter and area of a
triangle.
Triangles
• A 3-sided figure
• named by the three points  ABC
• endpoints are called vertices of the
triangle
B
A
C
3
4
3
4
Isosceles
3
All sides equal
4
Scalene
2
Two sides equal
6
5
3
Right
8
No sides equal
4
o
Has a 90 angle; special properties
Definition
Notes about Right Triangles
leg
– The sides of the triangle that create
the right angle are called the legs
– The side of the triangle that is opposite
the right angle is called the hypotenuse
leg
Definition
Notes about Isosceles Triangles
– The congruent sides of the triangle are
called the legs
– The third side of the triangle is called
the base
base
Isosceles
Scalene
Right
EXAMPLE #1
FIND THE PERIMETER
P = s1 + s2 + s3
4 cm
6 cm
8 cm
P=4+6+8
P = 18 cm
EXAMPLE #2
The perimeter of the triangle is 16
in.
A) What is x?
B) What are the side lengths?
x
x
A) P = s1 + s2 + s3
16 = x + x + (x – 2)
x2
16 = 3x - 2
2) 6 in, 6 in, 4 in
18 = 3x
6=x
PRACTICE #1
1. Find the perimeter of the triangle.
8 ft
10 ft
6 ft
2. Find the length of the hypotenuse
if the perimeter is 12 inches.
x
X+2
X+1
Area of a Triangle
• The formula for the area of a triangle is
b = base
h = height
1
A  bh
2
h
b
Notice the base
and the height
form the 90⁰ angle
Height/Altitude
• Height is also called an altitude
• Altitude: a line segment that connects a
vertex to the base forming a 90⁰ angle.
h
h
h
Width = Height
Where does the area formula come from?
Length = Base
Area Rectangle =
lxw
Width = Height
1
A  bh
2
Length = Base
What shapes do you see?
Two triangles
How much area does one triangle
make-up of the rectangle?
½
EXAMPLE #3
Find the area of the triangle
6
1
A  bh
2
1
 12  8
2
 68
 48 units2
9
8
12
EXAMPLE #4
x+1
Base = 5 cm
x
The area of the triangle above is 15 cm2.
1) What is the height?
2) What is the base?
1
A  bh
2
1
15  ( x )( x  1)
2
Height = 6 cm
1 2
15  ( x  x)
2
1 2
15  ( x  x)
2
30  ( x2  x)
x 2  x  30  0
( x  6)( x  5)  0
x = -6 x = 5
EXAMPLE #5
6 ft
6 ft
10 ft
10 ft
What is the area of the unshaded region?
Unshaded region = Area of rectangle – 2( Area of triangle)
Area of rect. = (l x w) = (20)(6) = 120
Area of triangles = 2 (½bh ) = 2( ½)(6)(10) = 60
Area of unshaded = 120 – 60 = 60 ft2
Pythagorean Theorem
a b  c
2
2
2
c
a
b
• The
Pythagorean Theorem is only used with a right triangle.
• c represents the hypotenuse.
• a and
b are the legs of the triangle
EXAMPLE #6
Find the area.
15 mm
12 mm
First find the missing side length
x
12  x  15
x  81
144 x  225
x  9mm
2
2
2
2
A =½ (9)(12) = 54 mm²
2
PRACTICE #2
1. The length of the base of a triangle is 3 cm and the
height is 2 cm. What is the area of the triangle?
2. Find the area of the shaded region.
3.6 in.
4 in.
http://www.youtube.com/watch?gl=GB&hl=enGB&v=o2Z6tDSb6c8&feature=related
Triangle song – sesame street