Hello!
The formula to find the surface area of a pyramid is as follows:
[tex] \frac{1}{2} [/tex] 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 [tex] \frac{1}{2} [/tex] pl + B and with the values we just found plugged in it becomes [tex] \frac{1}{2} [/tex] (10)(3) + (6.25).
And now all we have to do is solve!
[tex] \frac{1}{2} [/tex] (10)(3) + (6.25)
[tex] \frac{1}{2} [/tex] (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!
