Robert is always curious in creating formulas, for solving mathematical problems, of his own by repeated trial and error method. One day he found a formula for finding the surface area of the hexagonal pyramid. What should be the correct formula for the surface area of the hexagonal pyramid?


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Answer:

^@ 3(bh + ab) ^@

Step by Step Explanation:
  1. The given figure can be broken into the small figures as shown below. The area of the individual figure can be calculated and added to get the surface area of the hexagonal pyramid.
    ^@=^@ b h ^@ \times ^@^@6^@^@ + ^@ b a
  2. Area of bigger triangle ^@ = \left( \dfrac{ 1 }{ 2 } \times b \times h \right) ^@
    Also, the area of the hexagon can be divided into ^@6^@ small triangles.
    So, the area of a smaller triangle in the hexagon ^@ = \left( \dfrac{ 1 }{ 2 } \times b \times a \right) ^@
  3. So, the combined surface area of the figure can be calculated as: @^\begin{align} & 6 \left( \dfrac{ 1 }{ 2 } \times b \times h \right) + 6 \left( \dfrac{ 1 }{ 2 } \times b \times a \right) \\ = & 3bh + 3ab \\ = & 3(bh + ab) \end{align}@^

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