Question

NO LINKS!!!! Find the Lateral Area, Total Surface Area, and Volume. Round your answer to two decimal places.​

Answer 1

#1

• l=6
• b=4
• h=10

LsA

• 2×h(l+b)
• 2(10)(6+4)
• 200.00m²

TSA

• 2(lb+bh+lh)
• 2(6×4+4×10+10×6)
• 2(24+40+60)
• 248.00m²

Volume.

• lbh
• 10(6)(4)
• 240m³

#2

• l=5ft
• b=8ft

LSA

• 3lb
• 2(5)(8)
• 120ft²

TSA

Hypotenuse=√5²+8²=√89=9.4

• 5(8)+9.4(12)+12(8)+5(12)
• 40+112.8+96+60
• 308.8ft²

Volume

• Area of base×Height
• 1/2(5)(8)(12)
• 20(12)
• 240ft³

Answer 2

Lateral Surface Area: The total surface area of a three-dimensional object, excluding the bases.

Question 5

Figure: Rectangular prism

Given:

• length (
  `l`) = 10 m
• width (
  `w`) = 4 m
• height (
  `h`) = 6 m

Lateral Surface Area

`\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}`

Total Surface Area

`\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}`

Volume

`\begin{aligned}\textsf{Volume of a rectangular prism} & = whl\\\implies \sf T.A. & = 4 \cdot 6 \cdot 10\\& = 240\:\: \sf m^3\end{aligned}`

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
`a^2+b^2=c^2` where a and b are the legs and c is the hypotenuse.

`\implies 5^2+8^2=c^2`

`\implies c^2=89`

`\implies c=√(89)`

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.

`\begin{aligned}\implies \sf L.A. & = \sf 12(8+5+√(89))\\& = \sf 269.21\:\:ft^2\end{aligned}`

Total Surface Area

The T.A. is made up of the L.A. plus the areas of the triangular bases.

`\begin{aligned}\textsf{Area of a triangle} & = (1)/(2)bh\\\implies \sf A & = (1)/(2) \cdot 8 \cdot 5\\& = 20\:\: \sf ft^2\end{aligned}`

`\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}`

Volume

`\begin{aligned}\textsf{Volume of a triangular prism} & = \sf base\:area * height\\\implies \sf Vol. & = 20 \cdot 12\\& = 240\:\: \sf ft^3\end{aligned}`