Question

find the lateral area and volume of the right triangular prism
this is where i got to :/ help
s=2B+PH
S=2B+(4m)+(3m)
s=2B+15m

Answer 1

For the volume, note that, by definition, it is base area times height.
Hence, we have:
\[
Bh=V
\]But, also note that the base is a right triangle whose area is:
\[
B=\frac{1}{2}lw
\]Using this, we get, for the volume:
\[
\frac{1}{2}lwh=\frac{1}{2}3\cdot4\cdot6=36\text{ m}^3
\]

Answer 2

Note that, for the surface area, we have a right triangle and a rectangle as unique shapes.
The area for each (denoted \(A_1, A_2, A_3, A_4\) respectively) is:
\[
A_1=\frac{1}{2}bh\\
A_2=lw\\
A_3=lw
\]Plugging in the values, we get:
\[
A_1=\frac{1}{2}3\cdot4=6\\
A_2=4\cdot6=24
\]Notice that a right triangle has a hypotenuse (the side of the latter rectangle) length of:
\[
c^2=a^2+b^2\implies\\
c=\sqrt{a^2+b^2}
\]So:
\[
c^2=3^2+4^2=25\implies\\
c=5
\]Noting this, we get a third area of:
\[
A_3=5\cdot6=30
\]And, a fourth area of:
\[
A_4=3\cdot6=18
\]The area \(A_1\) is repeated twice (there are two triangles), so, for our total area, we have:
\[
A_t=2A_1+A_2+A_3+A_4
\]

Answer 3

i get how you got the volume but im a bit confused on the surface area part