Answer:
• (,a)Triangular Prism
,• (b)Lateral Surface Area= 36 cm²
,• (c)Total Surface Area= 48 cm²
Explanation:
(a)The figure has a triangle as its uniform cross-section. Thus, it is a triangular prism.
(b)Lateral Surface Area
The lateral surface area is the area of the sides of the prism, i.e. excluding the uniform top and base.
The sides of the triangular prism consist of the three rectangles.
[tex]\begin{gathered} \text{Lateral Surface Area}=\text{Area of Rect. 1+Area of Rect. 2+Area of Rect. 3} \\ =(3\times4)+(3\times3)+(3\times5) \\ =12+9+15 \\ =36\;cm^2 \end{gathered}[/tex]The lateral surface area is 36 cm squared.
(c)Total Surface Area
To find the total surface area, add the area of the top and base to the lateral surface area.
The top and base are the two right-triangles with a base of 3 cm and a height of 4cm.
[tex]\begin{gathered} \text{ Total Surface Area=Lateral Surface Area+2\lparen Area of Triangles\rparen} \\ =36+2(\frac{1}{2}\times3\times4) \\ =36+12 \\ =48\;cm^2 \end{gathered}[/tex]The total surface area is 48 cm squared.