Question

The height (OC) of a square pyramid shaped toy with all equal edges of dimension 12 in is in.

• A. $\frac{6}{\sqrt{2}}$
• B. $6\sqrt{2}$
• C. $3\sqrt{2}$
• D. $3\sqrt{2}$

Answer 1

The correct option is B $6\sqrt{2}$

In the given figure,

Triangle OAB is a right angle triangle,
$OA=12$
$AB=\frac{12}{2}=6$
Using pythagoras theorem,

$O{A}^2=A{B}^2+B{O}^2$

${12}^2=6^2+B{O}^2$

$144-36=B{O}^2$

$108=B{O}^2$

Similarly,
Triangle OBC is a right angle triangle,
$B{O}^2=O{C}^2+B{C}^2$

and $BC=\frac{12}{2}=6$

$\Rightarrow 108=O{C}^2+6^2$

$O{C}^2=108-36$

$OC=\sqrt{72}$

$OC=\sqrt{6\times 6\times 2}$

$OC=6\sqrt{2}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ∴$\text{Height of square pyramid =}6\sqrt{2}in$