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Mathematics
Problem
Which of the following is the correct algebraic form of Heron’s formula for the area
Δ
\Delta
Δ
of a triangle with sides
a
a
a
,
b
b
b
,
c
c
c
and semi-perimeter
s
s
s
? a)
Δ
=
1
2
a
b
sin
C
\Delta = \tfrac{1}{2}ab\sin C
Δ
=
2
1
ab
sin
C
b)
Δ
=
s
(
s
−
a
)
(
s
−
b
)
(
s
−
c
)
\Delta = s(s-a)(s-b)(s-c)
Δ
=
s
(
s
−
a
)
(
s
−
b
)
(
s
−
c
)
c)
Δ
=
s
(
s
−
a
)
(
s
−
b
)
(
s
−
c
)
\Delta = \sqrt{s(s-a)(s-b)(s-c)}
Δ
=
s
(
s
−
a
)
(
s
−
b
)
(
s
−
c
)
d)
Δ
=
(
a
+
b
+
c
)
(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
\Delta = \sqrt{(a+b+c)(a+b-c)(b+c-a)(c+a-b)}
Δ
=
(
a
+
b
+
c
)
(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
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