Answer:
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:
[tex]\text{Width of the prism,}x=\frac{1}{2}\times8.26=4.13\; m[/tex]
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:
[tex]\begin{gathered} \text{Surface Area}=2(\frac{1}{2}bh)+2(LW)+lw \\ =2\times\frac{1}{2}\times4.13\times2.6+2(3.2\times8.26)+(8.26\times4.13) \\ =10.738+52.564+34.1138 \\ =97.4158 \\ \approx97.416\; m^2 \end{gathered}[/tex]
The surface area of the prism is 97.416 m² (correct to 3 decimal places).
