2009-II-17

Ans: B
The length of a side of the base square

$\begin{array}{cl}
= & 48 \div 4 \\
= & 12 \text{ cm}
\end{array}$

Therefore, the base area

$\begin{array}{cl}
= & 12^2 \\
= & 144\text{ cm}^2
\end{array}$

Note that the base of the solid right pyramid is a square, then all the slant faces are identical. By applying the Heron’s formula to one of the slant faces, we have

$\begin{array}{rcl}
s & = & \dfrac{10 + 10 + 12}{2} \\
& = & 16 \text{ cm}
\end{array}$

Therefore, the area of a slant face

$\begin{array}{cl}
= & \sqrt{16(16-10)(16-10)(16-12) } \\
= & 48\text{ cm}^2
\end{array}$

Therefore, the total surface area of the pyramid

$\begin{array}{cl}
= & 48 \times 4 + 144 \\
= & 336\text{ cm}^2
\end{array}$