Question

The pencil below is in the shape of a regular hexagonal

prism joined to a hexagonal pyramid.
The area of the cross-section of the prism is 314.4 mm².
Work out the total surface area of the pencil.
If your answer is a decimal, give it to 1 d.p.
11 mm
70 mm
17 mm

Answer 1

so hmm we know the cross-section area, so we can say that the left-hand-side of the pencil is 314.4 mm², now how about the rest? Well, the rest is just the area of six 11x70 rectangles and six triangles whose base is 11 and height is 17.

`\stackrel{ \textit{\LARGE Areas} }{\stackrel{\textit{left-side section}}{314.4}~~ + ~~\stackrel{\textit{6 rectangles}}{(6)(11)(70)}~~ + ~~\stackrel{\textit{6 triangles}}{6\left[\cfrac{1}{2}(\underset{b}{11})(\underset{h}{17}) \right]}} \\\\\\ 314.4+4620+561\implies \text{\LARGE 5495.4}~mm^2`