# The question is below?

## A square based pyramid is on the top of cuboid having length and breadth equal to 6 cm and height equal to 10 cm. If the TSA of the combined solid object is $336 c {m}^{2}$ then find the height of the pyramid.

Jun 7, 2018

Here the base of the pyramid must be $6 \times 6 c {m}^{2}$ square.

If the height of the pyramid be $h$ cm,then the height of each triangular side of the pyramid will be $b = \sqrt{{h}^{2} + {3}^{2}}$cm. Base of each triangular face being $6$ cm the total surface area of 4 triangular face will be $= 4 \cdot \frac{1}{2} \cdot 6 \cdot \sqrt{{h}^{2} + {3}^{2}}$

$= 12 \sqrt{{h}^{2} + {3}^{2}} c {m}^{2}$

So total area of other 5surfaces will be $= \left(4 \cdot 6 \cdot 10 + {6}^{2}\right) = 276 c {m}^{2}$

Hence by the problem

$12 \sqrt{{h}^{2} + {3}^{2}} + 276 = 336$

$\implies 12 \sqrt{{h}^{2} + {3}^{2}} = 60$

$\implies \sqrt{{h}^{2} + {3}^{2}} = 5$

$\implies {h}^{2} + 9 = 25$

$\implies h = \sqrt{16} = 4$ cm