Answer to Question #149990 in Trigonometry for yui

Question

PROBLEM 2. A pyramidal monument has an octagonal base, each side of which is 2 m. Each lateral edge of the pyramid is 3m. Find the total cost of painting the lateral surface of the monument at PhP 730.00 per square meter?
FINAL ANSWER: _______________________________________

Answer 1

$S=8\cdot S_1$ is the area of the lateral surface of the monument

$S_1$ is the area of one side of the monument

$P_1=730\space PhP$ is the price per square meter

$P=S\cdot P_1$ is the total cost of painting the lateral surface of the monument

$S_1=\sqrt{p\cdot(p-a)\cdot(p-b)\cdot(p-c)}$

$a=b=3$m

$c=2m$

$p=\frac {a+b+c}2=\frac {3+3+2}2=4m$

$S_1=\sqrt{p\cdot(p-a)\cdot(p-b)\cdot(p-c)}=\sqrt{4\cdot(4-3)\cdot(4-3)\cdot(4-2)}=2\sqrt {2}m^2$

$S=16\sqrt{2}m^2$

$P=S\cdot P_1=16\sqrt{2}\cdot730\approx16518\space PhP$