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Mathematics
Problem
A plane makes intercepts
O
A
,
O
B
OA, OB
O
A
,
O
B
and
O
C
OC
O
C
whose measurements are
a
,
b
a, b
a
,
b
and
c
c
c
on the
O
X
,
O
Y
OX, OY
O
X
,
O
Y
and
O
Z
OZ
O
Z
axes. The area of triangle
A
B
C
ABC
A
B
C
is a.
1
2
(
a
b
+
b
c
+
c
a
)
\frac{1}{2}(ab + bc + ca)
2
1
(
ab
+
b
c
+
c
a
)
b.
1
2
a
b
c
(
a
+
b
+
c
)
\frac{1}{2}abc(a + b + c)
2
1
ab
c
(
a
+
b
+
c
)
c.
1
2
(
a
2
b
2
+
b
2
c
2
+
c
2
a
2
)
1
/
2
\frac{1}{2}(a^2b^2 + b^2c^2 + c^2a^2)^{1/2}
2
1
(
a
2
b
2
+
b
2
c
2
+
c
2
a
2
)
1/2
d.
1
2
(
a
+
b
+
c
)
2
\frac{1}{2}(a + b + c)^2
2
1
(
a
+
b
+
c
)
2
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