Pyramid surface area (total): Lateral surface area + Base area
Lateral surface area = [tex] \frac{2p*a}{2} [/tex] where p is the base perimeter and a the apothem.
The base is a sqaure so, find the area of the square.
Base Area = 16*16 = 256 in²
Calculate the perimeter = 16*4 = 64 in
LSA = (64*17)/2 = (64*17)/2 = 1088/2 = 544 in²
TSA = 544+256 = 800 in²
Total surface of cone: LSA + Base Area
LSA = πra
Let's find the apotheme. Apply Pitagora, again the hypothenuse is the apotheme. The legs are the radius and the height.
a = √8²+3² = √64+9 = √73 ≈ 8,5 in.
Base area (area of the circle) = πr² = 3²*π = 9π in²
LSA = 3*8,5*π = 25,5π in²
TSA = 25,5π+9π = 34,5π = 34,5*3,14 = 108,3 in²
