SOLUTION: The diagonal of the base of a regular square pyramid is 10 radical 2 and the altitude if the pyramid is 12. What is the lateral surface area of the pyramid rounded to the nearest s

Question 870943: The diagonal of the base of a regular square pyramid is 10 radical 2 and the altitude if the pyramid is 12. What is the lateral surface area of the pyramid rounded to the nearest square inch?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
As written, there are no units to the and length of the diagonal and height,
but I will assume the measurements are all in inches.
Looking at the base, from the bottom, it looks like this:
C is the center of the base; M and N are the midpoints of opposite sides of the base.
The side of the square base of the pyramid measures inches.
The diagonal length, in inches, is .
According to the Pythagorean theorem,

Cutting the pyramid into halves through the vertex and the middle of opposite sides,
the section would look look this:
V is the vertex of the pyramid; C is the center of the base; M and N are the midpoints of opposite sides of the base.
The slant height, measured from the midpoint of a side of the square base to the vertex, is inches.
According to the Pythagorean theorem,

The lateral surface of the pyramid is made of triangular sides.
Each of those triangles has a base measuring inches (the side of the square base of the pyramid),
and a height of inches (the slant height of the pyramid.
The area of a triangle is calculated as .
The total lateral surface area of the pyramid, in square inches, is

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