Answer to Question #149989 in Geometry 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

We have 8 triangles on surface of figure. So to find area of triangle, we need to find it's height:$h={\sqrt{3^{2}-1^{2}}}=\sqrt 8$

Area of triangle:

$A={{2 \cdot {\sqrt{8}}} \over 2}=2 \cdot {\sqrt 2}$

There are 8 triangles, so area of surface:

$8 \cdot {2 \cdot {\sqrt 2}}=16 \cdot {\sqrt 2}$

To find price:

$730 \cdot {16 \cdot {\sqrt 2}}=16518$

Answer: 16518