Question

The surface area of this regular pyramid is 1040 cm2. The base is a regular pentagon with side b = 16 cm and slant height l =15 cm. Find its apothem (a).
show work please. i will give brainliest ! :)

Answer 1

Answer:

(a) = 11 cm

Step-by-step explanation:

The formula for finding the surface area of a regular pyramid is B + (1/2*P*l), with B being the area of the base, p being the perimeter of the base, and l being the slant of the pyramid.

The area of a pentagon can be solved using the formula 1/2*a*p, with a being the apothem and p being the perimeter of the pentagon.

1. B + (1/2*80*15) = 1040
2. B + 600 = 1040
3. 1040 - 600 = 440 (440 is the area of pentagon)
4. 1/2*a*(16*5) = 440
5. 40*a = 440
6. 440/40 = 11

The apothem is 11 cm. Hope this helps!