Question

The base edge of a regular pentagonal prism is $6cm$ and its bases are $12cm$ apart. Find its volume in $cu.cm$.

• A. $743.22$
• B. $786.89$
• C. $567.45$
• D. $842.12$

Answer 1

The correct option is A $743.22$

Given : Side of regular pentagon $\left(a\right)=6cm$ height $\left(h\right)=12cm$

Area of regular pentagon $=\frac{1}{4}\sqrt{5(5+2\sqrt{5})}{a}^2$

$=\frac{1}{4}\sqrt{25+10\sqrt{5}}\times 36$

$=9\sqrt{47.36}=61.9367$

Volume of prism $=Basearea\times height$

$=61.9367\times 12=743.22cu.m$

Hence, option A is correct.