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Answer:
see explanation
Step-by-step explanation:
Parallel lines have equal slopes.
To find D and E use the midpoint formula
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( ,
)
Here (x₁, y₁ ) = A(4, 6) and (x₂, y₂ ) = B(2, - 2) , then
D = (,
) = (3, 2 ) and
let (x₁, y₁ ) = B(2, - 2 ) and (x₂, y₂ ) = C(- 2, - 4 ), then
E = ( ,
) = (1, 1 )
Use the slope formula to find slopes of DE and BC
m =
with (x₁, y₁ ) = D(3, 2) and (x₂, y₂ ) = E(1, 1), then
=
=
=
Repeat with (x₁, y₁ ) = B(2, - 2) and (x₂, y₂ ) = C(- 2, - 4), then
=
=
=
Since the slopes are equal then DE and BC are parallel lines
Check the picture below.
the "lateral" area, or "sides" area, is just the area of all the four triangular faces, and it doesn't include the bottom or base of the pyramid.
however, notice, each triangular face is really just a triangle with a base of 24, and a height of 16.
![\bf \left[\frac{1}{2}(\stackrel{b}{24})(\stackrel{h}{16}) \right]+\left[\frac{1}{2}(\stackrel{b}{24})(\stackrel{h}{16}) \right]+\left[\frac{1}{2}(\stackrel{b}{24})(\stackrel{h}{16}) \right]+\left[\frac{1}{2}(\stackrel{b}{24})(\stackrel{h}{16}) \right] \\\\\\ \textit{or just }\qquad 4\left[\frac{1}{2}(\stackrel{b}{24})(\stackrel{h}{16}) \right]\impliedby \textit{lateral area of the pyramid}](https://tex.z-dn.net/?f=%5Cbf%20%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%28%5Cstackrel%7Bb%7D%7B24%7D%29%28%5Cstackrel%7Bh%7D%7B16%7D%29%20%5Cright%5D%2B%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%28%5Cstackrel%7Bb%7D%7B24%7D%29%28%5Cstackrel%7Bh%7D%7B16%7D%29%20%5Cright%5D%2B%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%28%5Cstackrel%7Bb%7D%7B24%7D%29%28%5Cstackrel%7Bh%7D%7B16%7D%29%20%5Cright%5D%2B%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%28%5Cstackrel%7Bb%7D%7B24%7D%29%28%5Cstackrel%7Bh%7D%7B16%7D%29%20%5Cright%5D%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Bor%20just%20%7D%5Cqquad%204%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%28%5Cstackrel%7Bb%7D%7B24%7D%29%28%5Cstackrel%7Bh%7D%7B16%7D%29%20%5Cright%5D%5Cimpliedby%20%5Ctextit%7Blateral%20area%20of%20the%20pyramid%7D)
the "lateral" area, or "sides" area, is just the area of all the four triangular faces, and it doesn't include the bottom or base of the pyramid.
however, notice, each triangular face is really just a triangle with a base of 24, and a height of 16.