Answer to Question #142679 in Geometry for bhj

Question

A concrete monument is a regular pentagonal pyramid with base edge of
40 cm and one of its lateral edges measure 50 cm. if the height is 36.64cm and lateral surface is 916.52 centimeter squared.
1. How much concrete is needed to build the monument?

Answer 1

$h=36.64cm, a = 40cm$

find the base angles of one of the triangle as follows,

$\frac{360^{o}}{5} =72^{o}$

each base angle = $\frac{180^{o} - 72^{o}}{2}=54^{o}$

volume of the pentagonal pyramid is given by,

$V=\frac{5}{12}tan(54^{o})ha^{2}= \frac{5}{12}tan(54^{o})\times36.64\times40^{2}= 33,620.42cm^{3}$