Answer:
1604.4 sq. cm.
Explanation:
The base of the solid is a regular hexagon.
A regular hexagon can be divided into 6 equilateral triangles.
• Base of one of the triangles, s = 14 cm
,
• Height of one of the triangles, a = 12.1 cm
First, calculate the area of the hexagonal base.
[tex]\begin{gathered} \text{Area of the hexagonal base}=6\times\text{Area of one equilateral triangle} \\ =6\times\frac{1}{2}sa \\ =3\times14\times12.1 \\ =508.2\; cm^2 \end{gathered}[/tex]
Next, calculate the lateral surface area (area of the sides).
The side of the solid is made up of 6 rectangles with dimensions 7cm by 14cm.
[tex]\text{Lateral Surface Area}=6\times7\times14=588\; cm^2[/tex]
Therefore, the surface area of the solid will be:
[tex]\begin{gathered} \text{Total Surface Area=Area of the Top+Area of the base+Lateral Area} \\ =508.2+508.2+588 \\ =1604.4\; cm^2 \end{gathered}[/tex]
The total surface area is 1604.4 sq. cm.
