Surface AreaLet a , b , c , and d be positive real numbers. The portion of the plane a x + b y + c z = d in the first octant is shown in the figure. Show that the surface area of this portion of the plane is equal to A ( R ) c a 2 + b 2 + c 2 where A ( R ) is the area of the triangular region R in the x y -plane, as shown in the figure.
Solution Summary: The author explains that the given portion has a surface area equal to A(R)csqrta2+b2. The area of tri
Surface AreaLet
a
,
b
,
c
, and
d
be positive real numbers. The portion of the plane
a
x
+
b
y
+
c
z
=
d
in the first octant is shown in the figure. Show that the surface area of this portion of the plane is equal to
A
(
R
)
c
a
2
+
b
2
+
c
2
where
A
(
R
)
is the area of the triangular region
R
in the
x
y
-plane, as shown in the figure.
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