Question #149990
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: _______________________________________
1
Expert's answer
2020-12-15T17:31:23-0500

S=8S1S=8\cdot S_1 is the area of the lateral surface of the monument

S1S_1 is the area of one side of the monument

P1=730 PhPP_1=730\space PhP is the price per square meter

P=SP1P=S\cdot P_1 is the total cost of painting the lateral surface of the monument

S1=p(pa)(pb)(pc)S_1=\sqrt{p\cdot(p-a)\cdot(p-b)\cdot(p-c)}

a=b=3a=b=3m

c=2mc=2m

p=a+b+c2=3+3+22=4mp=\frac {a+b+c}2=\frac {3+3+2}2=4m

S1=p(pa)(pb)(pc)=4(43)(43)(42)=22m2S_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=162m2S=16\sqrt{2}m^2

P=SP1=16273016518 PhPP=S\cdot P_1=16\sqrt{2}\cdot730\approx16518\space PhP


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