Question

Find the height (OC) of a square pyramid shaped toy with all equal edges of dimesion 15 in.

• A. $\frac{15}{\sqrt{2}}$
• B. $15\sqrt{2}$
• C. $\frac{10}{\sqrt{2}}$
• D. $5\sqrt{2}$

Answer 1

The correct option is A $\frac{15}{\sqrt{2}}$

In the given figure,
Triangle OAB is a right angle triangle,
$OA=15$
$AB=\frac{15}{2}$
Using pythagoras theorem,

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

${15}^2=(\frac{15}{2}{)}^2+B{O}^2$

$225-\frac{225}{4}=B{O}^2$

$\frac{675}{4}=B{O}^2$

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

and $BC=\frac{15}{2}$

$\Rightarrow \frac{675}{4}=O{C}^2+(\frac{15}{2}{)}^2$

$O{C}^2=\frac{450}{4}$

$\Rightarrow OC=\frac{15}{\sqrt{2}}$


<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ∴$\text{Height of square pyramid =}\frac{15}{\sqrt{2}}$