Question

A square-based pyramid is placed on a square-based prism with the same base $14$cm. If the height of the prism is $9$cm and height of the pyramid is $7$cm, find the total surface area of the solid obtained by joining them.

Answer 1

TSA of solid = TSA square base pyramid + TSA of prism

TSA of pyramid = $4\times \frac{1}{2}\times AE\times CD+{\left(14\right)}^2$

= $(2\times 7\sqrt{2}\times 14)+196$

= $196(\sqrt{2}+1){cm}^2$

= $472.36{cm}^2$

TSA of Prism $=LSA+2\left(areaofbase\right)$

= (Perimeter of base $\times$ h) + 2${\left(14\right)}^2$

= $(4\times 14\times 9)+392$

= $504+392=896{cm}^2$

$\therefore$ TSA of solid $=472.36+896$ = $1368.36c{m}^2$