Ill give u legit brainliest, a and 5 stars only if its the correct answer.

The answer is:  "527.52 [square yards]".

Explanation:


Surface Area (S.A. of a cone) = π *r * (r + √(h² + r²) .

in which:  π = 3.14 (as instructed in the given problem; 

                r = radius = diameter / 2 = 14 yd / 2 = 7 yd.

(Note: diameter = 14 yd ; given in the figure shown) ;
                 
                h = perpendicular height = ??

Let us use the Pythagorean theorem to determine "h"
                                                              (the perpendicular height);

 a² + b² = c² ; in which "c" in the hypotenuse; 

c = 17 yd. (the "slant length" of the cone; given in the figure;

Let: "b" = the radius, "r" = 7 yd; 

Solve for "a"; which is the "perpendicular height" ; or "h" ;

→ a² + b² = c² ;

→ a² = c² − b² ;

→ Plug in our known values for "c" and "b" ; to solve for "a" ;

→ a² = 17² − 7²  = 289 − 49 = 240 ;

→ a² = 240 ; 

Take the positive "square root" of each side of equation; to isolate "a" on one side of the equation" and to solve for "a" ; 

→√(a²) = √240 ;

→ a = 15.4919333848296675 ; = "h" ; perpendicular height; 
For now, we can simply refer to: "h" as equal to: "(√240)" ;

Now, given the formula for the surface area of a cone:

→ " Surface Area (S.A. of a cone) = π *r * (r + √(h² + r²) " ; 

Plug in our known values; and solve:

→Surface Area (S.A. of a cone) = 

      3.14 * (7 yd) * { 7 yd + √[(√240)² + (7 yd)²] } ;

            = 3.14 * (7 yd) * { 7 yd + √[(240 + (49 yd²] } ;

            = 3.14 * (7 yd) * { 7 yd + √289 yd²} ;

            = 3.14 * (7 yd) * ( 7 yd + 17 yd) ;

            = 3.14 * (7 yd) * (24 yd) 

            = 527.52 yd²  ; or write as: "527.52 square yards".