Question 1:

If x = 13 units, y = 24 units, z = 22 units, and h = 5 units, then what is the surface area of the triangular prism shown above? *

○ [tex]\bm{A.}[/tex] [tex]\sf{ \: 6,864 units^2}[/tex]

○ [tex]\bm{B.}[/tex] [tex]\sf{1,220 \: units^2}[/tex]

○ [tex]\bm{C.}[/tex] [tex]\sf{956 \: units^2}[/tex]

○ [tex]\bm{D.}[/tex] [tex]\sf{ 1,320 \: units^2}[/tex]

[tex]\large\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}[/tex]

To find the surface area of a triangular prism let's apply this formula:

[tex]\boxed{\tt \: { SA = Pl + 2B}}[/tex]

Where:

• [tex]\small{\longrightarrow\tt{\green{P= \: Perimeter \: of \: triangle \: base}}}[/tex]
• [tex]\longrightarrow\tt{\green{L= \: Length \: the \: prism}}[/tex]
• [tex]\longrightarrow\tt{\green{B= \: Area \: of \: Triangular Base. }}[/tex]

Now we have the following:

[tex]\longrightarrow \tt{ P=x+x+y=13+13 + 24 = 50}[/tex]

[tex]\longrightarrow\boxed{ \tt{L = 22}}[/tex]

For the area of the triangular base, let's apply the formula for the area of a triangle:

[tex]\longrightarrow \tt{ 2B = 2( \cfrac{1}{2} \cdot y \cdot h)}[/tex]

[tex]\longrightarrow \tt{= 2(60)}[/tex]

[tex]\longrightarrow\boxed{ \tt{= 120}}[/tex]

Therefore, to find the surface area, we have:

[tex]\boxed{\tt \: { SA = Pl + 2B}}[/tex]

[tex]\longrightarrow \sf SA = 50(22) + 120[/tex]

[tex]\longrightarrow \boxed{\tt \purple{SA= 1100+ 120 = 1,220 \: units^2}}[/tex]

Hence, the surface area of the triangular prism is 1,220 units².

Credits to: [tex] \bm{Savv \: Theo}[/tex]