Question

Hello, can someone help me with this?Question: The width of this prism's base is half it's length. Calculate it's surface area to 3 decimal places.

Answer 1

97.416 m²

Explanation:

From the diagram:

• The length of the prism = 8.26 m

Given that the width of this prism's base is half its length, then:

`\text{Width of the prism,}x=(1)/(2)*8.26=4.13\; m`

Next, the calculation of the surface area is required.

The triangular prism has 5 faces with the following dimensions.

• Two equal triangular faces with ,Base, b=4.13 m and Height, h =2.6m.

,

• Two rectangular faces at the side with dimensions: W=3.2m, L=8.26m.

,

• Base rectangular face with dimension l=8.26m, w=4.13m.

Therefore:

`\begin{gathered} \text{Surface Area}=2((1)/(2)bh)+2(LW)+lw \\ =2*(1)/(2)*4.13*2.6+2(3.2*8.26)+(8.26*4.13) \\ =10.738+52.564+34.1138 \\ =97.4158 \\ \approx97.416\; m^2 \end{gathered}`

The surface area of the prism is 97.416 m² (correct to 3 decimal places).