Question

Find the surface area of a square pyramid whose base edge is 6cm and whose slant edge is 5cm

Answer 1

Check the picture below.

so let's notice, the base is a 6x6 square, and triangular faces have a base of 6 and an altitude/height of 5. So we can just get the area of the square and the triangles and sum them up and that's the area of the pyramid.

`\bf \stackrel{\textit{triangles' area}}{4\left[ \cfrac{1}{2}(6)(5) \right]}+\stackrel{\textit{square's area}}{(6\cdot 6)}\implies 60+36\implies 96`

Answer 2

For this case we have that by definition, the surface area of a regular pyramid, is given by:

`SA = \frac {1} {2} p * l + B`

Where:

p: Represents the perimeter of the base

l: The inclination height

B: The area of the base

Now, since the base is square we have:

`B = 6 ^ 2 = 36 \ cm ^ 2\\p = 6 + 6 + 6 + 6 = 24 \ cm\\l = 5 \ cm`

Then, replacing the values:

`SA = \frac {1} {2} 24 * 5 + 36\\SA = 60 + 36\\SA = 96 \ cm ^ 2`

ANswer

`96 \ cm ^ 2`