Question

A monument has the shape of a square pyramid. The base has a length of 6ft. The height of a face is 13ft. What is the surface area of the pyramid

Answer 1

Hello!

The answer is:

The total surface area of the pyramid is:

`TotalSurfaceArea=192ft^(2)`

Why?

To calculate the surface area of a square pyramid, we need to use the following formula:

`TotalSurfaceArea=(1)/(2)pl+BaseArea`

Where,

p, is the perimeter of the base.

l, is the slant of the pyramid.

Base area, is the area of the square base.

Now, from the statement we know that the base has a length of 6 feet, and the height of a face (slant) is 13 feet.

So, calculating, we have:

`BaseArea=BaseLength^(2)=(6ft)^(2) =36ft^(2)`

`Perimeter=4*side=4*6feet=24feet`

The total surface area will be:

`TotalSurfaceArea=(1)/(2)l+BaseArea`

`TotalSurfaceArea=(1)/(2)*24ft*13ft+36ft^(2)`

`TotalSurfaceArea=156ft^(2)+36ft^(2)=192ft^(2)`

Hence, we have the total surface area of the pyramid is:

`TotalSurfaceArea=192ft^(2)`

Have a nice day!