We must use Pythagorean Theorem in order to find the the height of the cone in order to use the surface area of a cone formula. The formula that you use would be A=πr(r+h2+r2). You already have the radius which is 5.
Pythagorean Theorem
a^2 + b^2 = c^2
You have two leg measurements of the triangle, one of which is the hypotenuse. The hypotenuse is 21.
a^2 + (5)^2 = (21)^2
a^2 +25 = 441
Subtract 25
a^2 = 416
a = 20.4
Take the square root of 416 and you get about 20.4. So the height of the cone would be about 20.4.
πr(r+h2+r2) ----> π(5)(5+(20.4)2+(5)2) and you get about 408.47
