Triangles;Triangles;Objective: To find the Objective: To find the perimeter and area of perimeter and area of

a triangle.a triangle.

Triangles;Triangles;Objective: To find the Objective: To find the perimeter and area of perimeter and area of

a triangle.a triangle.

Triangles• A 3-sided figure• named by the three points• endpoints are called vertices of the

triangle

A

B

C

ABC

3

3

3

534

48

6

Equilateral

RightScalene

Isosceles

44

2All sides equalTwo sides equal

No sides equal Has a 90o angle; special properties

TRIANGLES

DefinitionNotes about Right Triangles

– 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

hypotenuse

leg

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

leg

leg

base

Equilateral

RightScalene

Isosceles

TRIANGLES

EXAMPLE #1FIND THE PERIMETER

4 cm

8 cm

6 cm P = 4 + 6 + 8

P = 18 cm

P = s1 + s2 + s3

The perimeter of the triangle is 16 in.A) What is x?B) What are the side lengths?

2x

x x

16 = 3x - 2

18 = 3x 6 = x

2) 6 in, 6 in, 4 in

EXAMPLE #2

16 = x + x + (x – 2)

A) P = s1 + s2 + s3

PRACTICE #11. Find the perimeter of the triangle.

6 ft

8 ft10 ft

2. Find the length of the hypotenuse if the perimeter is 12 inches.

X + 1

xX + 2

Area of a Triangle

• The formula for the area of a triangle is

b = base h = height

h

b

Notice the base and the height form the 90⁰

angle

bhA2

1

Height/Altitude

hh h

• Height is also called an altitude

• Altitude: a line segment that connects a vertex to the base forming a 90⁰ angle.

Where does the area formula come from?

Length = Base

Wid

th =

Heig

ht

Area Rectangle = l x w

Length = Base

Wid

th =

Heig

ht

What shapes do you see?

How much area does one triangle make-up of the rectangle?½

Two triangles

bhA2

1

8

12

6 9

1

2A b h

112 8

2

6 8

248 units

EXAMPLE #3Find the area of the triangle

x + 1

x The area of the triangle above is 15 cm2.1)What is the height?2)What is the base?

1

2A b h

230 ( )x x

2 30 0x x

( 6)( 5) 0x x

x = -6

x = 5

Base = 5 cm

Height = 6 cm

EXAMPLE #4

)1)((2

115 xx

)(2

115 2 xx

)(2

115 2 xx

10 ft 10 ft

6 ft6 ft

What is the area of the unshaded region?

Unshaded region = Area of rectangle – 2( Area of triangle)

= 60 ft2

Area of triangles = 2 (½bh ) = 2(

EXAMPLE #5

Area of rect. = (l x w) = (20)(6) = 120

½)(6)(10) = 60Area of unshaded = 120 – 60

Pythagorean Theorem

b

a c

• The Pythagorean Theorem is only used with a right triangle.• c represents the hypotenuse.• a and b are the legs of the triangle

222 cba

x

12 mm

15 mm

Find the area.

EXAMPLE #6

222 1512 x

225144 2 x

812 x

mmx 9

First find the missing side length

A = (9)(12) = 54 mm²½

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=en-GB&v=o2Z6tDSb6c8&feature=related

Triangle song – sesame street