α

2

b hA

perímetro

per a b c

1 2

2

cat catA

( )( )( )

2

Fórmula de Herão

A m m a m b m c

perímetroonde m

perímetro

per a b c

1 2

perímetro

per cat cat hip

per b c a

2 3

4A

3per

3

3

15(15− 5)(15− 12)(15− 13)

15(10)(3)(2)

900

2

2

dA

∆ABC ~ ∆ACH

𝑎

𝑏=𝑏

𝑚

𝑏

2= 𝑎.𝑚

∆ABC ~ ∆ABH

a

c=

c

n

𝑐2 = 𝑎.𝑛

∆ABH ~ ∆ACH

𝑏

𝑐=𝑚

ℎ=ℎ

𝑛

ℎ2 = 𝑚.𝑛

∆ABC ~ ∆ACH

a

b=

c

h

𝑎.ℎ = 𝑏. 𝑐

𝑚 + 𝑛 = 𝑎

𝑚 =𝑏2

𝑎 𝑛 =

𝑐2

𝑎

𝑏2

𝑎+𝑐2

𝑎= 𝑎

𝑏2 + 𝑐2

𝑎= 𝑎

𝑏2 + 𝑐2 = 𝑎2

𝒂𝟐 = 𝒃𝟐 + 𝒄𝟐

a = m. n

a = 18 + 32

𝑎 = 50

𝑏² = 𝑎.𝑚

𝑏² = 50.18

𝑏² = 900

𝑏 = 30

𝑐² = 𝑎.𝑛

𝑐² = 50.32

𝑐² = 1600

𝑐 = 40

𝑎.ℎ = 𝑏. 𝑐

50.ℎ = 30.40

ℎ =30.40

50

ℎ = 24

𝑐2 = 𝑎.𝑛

𝑐2 = 16.12

𝑐2 = 192

𝑐 = 192

𝑐 = 26 . 3

𝑐 = 22 . 22 . 22 . 3

𝑐 = 8 3

ℎ2 = 𝑚.𝑛

ℎ2 = 4.12

ℎ2 = 48

ℎ = 48

ℎ = 2222. 3

ℎ = 4 3

𝐵𝐻 = 𝑚

𝑚 = 16− 12

𝑚 = 4

h2 = m. n

h2 = 9.4

h2 = 36 h = 6

𝑎.ℎ = 𝑏. 𝑐

25.ℎ = 15.20

ℎ =15.20

25

ℎ = 12