Question

Give an example where usinh herons formula the area of a triangle coming 0​

Answer 1

In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria,[1] gives the area of a triangle when the length of all three sides are known. Unlike other triangle area formulae, there is no need to calculate angles or other distances in the triangle first.


A triangle with sides a, b, and c.

c.
Formulation Edit

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

A
=
s
(
s
−
a
)
(
s
−
b
)
(
s
−
c
)
,
A = \sqrt{s(s-a)(s-b)(s-c)},
where s is the semi-perimeter of the triangle; that is,

s
=
a
+
b
+
c
2
.
s=\frac{a+b+c}{2}.[2]
Heron's formula can also be written as

A
=
1
4
(
a
+
b
+
c
)
(
−
a
+
b
+
c
)
(
a
−
b
+
c
)
(
a
+
b
−
c
)
A=\frac{1}{4}\sqrt{(a+b+c)(-a+b+c)(a-b+c)(a+b-c)}
A
=
1
4
2
(
a
2
b
2
+
a
2
c
2
+
b
2
c
2
)
−
(
a
4
+
b
4
+
c
4
)
A=\frac{1}{4}\sqrt{2(a^2 b^2+a^2c^2+b^2c^2)-(a^4+b^4+c^4)}
A
=
1
4
(
a
2
+
b
2
+
c
2
)
2
−
2
(
a
4
+
b
4
+
c
4
)
A=\frac{1}{4}\sqrt{(a^2+b^2+c^2)^2-2(a^4+b^4+c^4)}
A
=
1
4
4
(
a
2
b
2
+
a
2
c
2
+
b
2
c
2
)
−
(
a
2
+
b
2
+
c
2
)
2
{\displaystyle A={\frac {1}{4}}{\sqrt {4(a^{2}b^{2}+a^{2}c^{2}+b^{2}c^{2})-(a^{2}+b^{2}+c^{2})^{2}}}}