Answer:
To find the surface area of a pyramid, we need to use the formula:
Surface Area = Base Area + [ (Perimeter of Base) x (Slant Height) ] / 2
Assuming the base of the pyramid is a square with sides of length 9in, the Base Area = 9in x 9in = 81in²
To find the slant height, we need to use the Pythagorean theorem:
( Slant Height )² = ( Height )² + ( 1/2 Base )²
( Slant Height )² = ( 9/2 )² + ( 9/2 )²
( Slant Height )² = 81/4 + 81/4
( Slant Height )² = 162/4
( Slant Height )² = 40.5
Slant Height = sqrt( 40.5 ) = 6.36in (rounded to two decimal places)
Perimeter of Base = 4 x Base = 4 x 9in = 36in
Now we can plug these values into the formula:
Surface Area = 81in² + [ ( 36in ) x ( 6.36in ) ] / 2
Surface Area = 81in² + ( 228.96in² ) / 2
Surface Area = 81in² + 114.48in²
Surface Area = 195.48in²
Rounding to the nearest tenth gives us answer A. O 187.1 in²