Question

Find the total area for the regular pyramid. T.A. xxx(sqr) + xx (sqr)x

Answer 1

We are to solve the total area of the pyramid and this can be done through area addition. We first determine the area of the base using the Heron's formula.
                           A = √(s)(s - a)(s - b)(s - c)
where s is the semi-perimeter
                                 s = (a + b + c) / 2
 Substituting for the base,
                               s = (12 + 12 + 12)/ 2 = 18
                          A = (√(18)(18 - 12)(18 - 12)(18 - 12) = 62.35
Then, we note that the faces are just the same, so one of these will have an area of,
                                s = (10 + 10 + 12) / 2 = 16
                                  A = √(16)(16 - 12)(16 - 10)(16 - 10) = 48
Multiplying this by 3 (because there are 3 faces with these dimensions, we get 144. Finally, adding the area of the base,
                          total area = 144 + 62.35 = 206.35