Answer to Question #141950 in Geometry for 56

Question

A concrete monument is a regular pentagonal pyramid with base edge of
40 cm and one of its lateral edges measure 50 cm.
1. What is the monument’s altitude?
2. If the lateral surface of the monument is to be covered with glass,
how much glass is needed?

Answer 1

a = 40cm , l = 50cm

1) $R= a/(2sin(180\degree/5)) = 40/(2sin 36\degree) = 34.026 cm$

$h = \sqrt{l^2 - R^2} = \sqrt{50^2 - 34.026^2} = 36.637 cm$

answer : 36.637 cm

2) $p = (a+l+l)/2 = 140/2 = 70$

$S = \sqrt{p(p-a)(p-l)(p-l)} = \sqrt{70*30*20*20} = 200\sqrt{21} = 916.52cm^2$

answer : 916.52 cm²