Problema Solution
the base of a pyramid is a rectangle, 50 cm by 34 cm. find the lateral area and volume if the altitude is 40 cm.
Answer provided by our tutors
Let
l = 50 cm
w = 34 cm
h = 40 cm
Using the Pythagorean Theorem we find that the lateral area A is calculated by the formula:
A = l*((w/2)^2 + h^2)^0.5 + w*((l/2)^2 + h^2)^0.5
A = 50((34/2)^2 + 40^2)^0.5 + 34((50/2)^2 + 40^2)^0.5
A = 3,776.91 cm^2
The lateral area is 3,776.91 cm^2.
The volume of the pyramid V is calculated by the following formula:
V = (1/3)l*w*h
V = (1/3)*50*34*40
V = 22,666.67 cm^3
The volume is 22,666.67 cm^3.