Question

In the accompanying regular pentagonal prism, suppose that each base edge measures 7 in. and that the apothem of the base measures 4.8 in. The altitude of the prism measures 10 in.A regular pentagonal prism and a pentagon are shown side by side. The pentagon contains a labeled segment and angle.The prism contains a horizontal top and bottom and vertical sides. The front left face and front right face meet the bottom base at right angles.The pentagon is labeled "Base".A line segment starts in the center of the pentagon, travels down vertically, and ends at the edge. The segment is labeled a.The vertical segment forms a right angle with the edge.(a)Find the lateral area (in square inches) of the prism.in2(b)Find the total area (in square inches) of the prism.in2(c)Find the volume (in cubic inches) of the prism.in3

Answer 1

To determine the lateral area of the prism;

`Lateral\text{ area=perimeter of the base}* height`
`Lateral\text{ area=5\lparen7\rparen }*10=350in^2`

To determine total area of the prism;

`Total\text{ area=2\lparen area of base\rparen+Lateral area}`
`\begin{gathered} Total\text{ area of the prism=2\lparen}(1)/(2)* perimeter\text{ of the base}* apotherm\text{\rparen+350} \\ \end{gathered}`
`\begin{gathered} Total\text{ area of the prism=2\lparen}(1)/(2)*5(7)*4.8\text{\rparen+380=168+350=518in}^2 \\ \end{gathered}`

To determine the volume of the prism;

`Volume\text{ = base area }* height`
`Volume=(1)/(2)*5(7)*4.8*10=840in^3`

Hence