Question

Find the surface area of a pyramid with base sides of 2.5 inches and a slant height of 3 inches.

Answer 1

Hello!

The formula to find the surface area of a pyramid is as follows: 
$\frac{1}{2}$ pl + B 

In this formula p represents the perimeter of the pyramid's base, l is the slant height, and B is the area of the base. 

So, we know that the length of the base sides is 2.5 inches and the slant height (or l) is 3 inches. 

The first thing we can do is solve for p or the perimeter of the base. To find the perimeter, you can either add up each of the sides or since it's a square just multiply the side length by 4; both of these options will give you the same answer. 
2.5+2.5+2.5+2.5 = 10       2.5*4 = 10
So, we now know that p = 10 inches. 

Next, we can solve for B or the area of the base. To do this, we take the length of the base * the width of the base, or in this case just 2.5*2.5; this gives us 6.25 inches
We now have the value of B which is 6.25 inches. 

Now that we have all the elements, we can plug the values into the formula! 

So, the formula originally is $\frac{1}{2}$ pl + B and with the values we just found plugged in it becomes $\frac{1}{2}$ (10)(3) + (6.25). 

And now all we have to do is solve! 
$\frac{1}{2}$ (10)(3) + (6.25)
$\frac{1}{2}$ (30) + (6.25). 
15 + (6.25). 
21.25

And there you have it! The surface area of a pyramid with base sides of 2.5 inches and a slant height of 3 inches is 21.25 inches. 

Hope you find this helpful!