Answer:
Lateral Surface Area: The total surface area of a three-dimensional object, excluding the bases.
Question 5
Figure: Rectangular prism
Given:
- length ([tex]l[/tex]) = 10 m
- width ([tex]w[/tex]) = 4 m
- height ([tex]h[/tex]) = 6 m
Lateral Surface Area
[tex]\begin{aligned}\textsf{L.A. of a rectangular prism} & = 2h(l+w)\\\implies \sf L.A. & = \sf 2 \cdot 6(10+4)\\& = \sf 168\:\:m^2\end{aligned}[/tex]
Total Surface Area
[tex]\begin{aligned}\textsf{T.A. of a rectangular prism} & = 2(lw+lh+wh)\\\implies \sf T.A. & = 2(10 \cdot 4+10 \cdot 6+4 \cdot 6)\\& = 248\:\: \sf m^2\end{aligned}[/tex]
Volume
[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = whl\\\implies \sf T.A. & = 4 \cdot 6 \cdot 10\\& = 240\:\: \sf m^3\end{aligned}[/tex]
Question 6
Figure: Triangular Prism
The bases of a triangular prism are the triangles.
First, find the hypotenuse of the right triangular base using Pythagoras' Theorem [tex]a^2+b^2=c^2[/tex] where a and b are the legs and c is the hypotenuse.
[tex]\implies 5^2+8^2=c^2[/tex]
[tex]\implies c^2=89[/tex]
[tex]\implies c=\sqrt{89}[/tex]
Lateral Surface Area
The L.A. is made up of 3 rectangles, each with a length of 12 ft and a width of one side of the triangular base.
[tex]\begin{aligned}\implies \sf L.A. & = \sf 12(8+5+\sqrt{89})\\& = \sf 269.21\:\:ft^2\end{aligned}[/tex]
Total Surface Area
The T.A. is made up of the L.A. plus the areas of the triangular bases.
[tex]\begin{aligned}\textsf{Area of a triangle} & = \dfrac{1}{2}bh\\\implies \sf A & = \dfrac{1}{2} \cdot 8 \cdot 5\\& = 20\:\: \sf ft^2\end{aligned}[/tex]
[tex]\begin{aligned}\implies \sf T.A. & = \sf L.A.+2\:base\:areas\\ & = 269.21+2(20)\\& = 309.21\:\: \sf ft^2\:(2\:d.p.)\end{aligned}[/tex]
Volume
[tex]\begin{aligned}\textsf{Volume of a triangular prism} & = \sf base\:area \times height\\\implies \sf Vol. & = 20 \cdot 12\\& = 240\:\: \sf ft^3\end{aligned}[/tex]
