formula de heron?

Question

show me an exercise and how you resolve please

Answer 1

You are given a triangle with two sides and the angle between them:

a = 5 cm
b = 6 cm
C = 78 degrees

Area = (1/2)*ab*sinC
=(1/2)(5)(6)*sin 78
=14.67 cm^2


Say they give you the three sides:

a = 3 cm
b = 4 cm
c = 5 cm

Define a number "s", called the semi-perimeter

s = (a + b + c) / 2

Area = sqrt[(s)(s - a)(s - b)(s - c)]



s = (3 + 4 + 5) / 2 = 6
=sqrt[(6)(6 - 3)(6 - 4)(6 - 5)]
=sqrt[(6*3*2*1)]
=sqrt[36]
=6 cm^2

Answer 2

This is also known as Hero's Formula and it's used to find the area of a triangle. If the sides of the triangle are called a, b, and c, then the 'semiperimeter' (s) is
s = (a+b+c)/2
and the area of the triangle is given by
A=√(s(s-a)(s-b)(s-c))

Lets say you have a triangle with sides 5m, 7m, and 8m. To find the area, calculate
s=(5+7+8)/2 = 10
Then the area is
A=√(10*5*3*2) = √300 = 17.32 square meters.

Hope that helps.


Doug

Answer 3

In geometry, Heron's formula states that the area of a triangle whose sides have lengths a, b and c is

Area = √[s (s-a) (s-b) (s-c)]
where
s = (a+b+c) / 2
Heron's formula can also be written
Area = [√(a+b+c) (a+b-c) (a+c-b) (b+c-a) ] / 4

Answer 4

what if the angle is unknown but the two sides were given and its area??