Answer:
800 ft²
Step-by-step explanation:
The total surface area of a square-base pyramid is given by the formula ...
A = s(s +2h) . . . . . . where s is the side length, h is the face slant height
In this problem, we need to find the slant height of a face in order to use this formula.
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slant height
The distance from the middle of one edge of the base to the peak of the pyramid is the slant height of a face of the pyramid. It is the hypotenuse of a right triangle whose legs are the pyramid height, and half the width of the base. For this pyramid, that is a right triangle with legs 15 and 8.
The Pythagorean theorem is used to find the hypotenuse of that triangle:
c² = a² +b² . . . . square of hypotenuse = sum of squares of legs
c² = 15² +8² = 225 +64 = 289
c = √289 = 17
The slant height of a face of the pyramid is 17 ft.
total area
The area formula tells us the total surface area is ...
A = s(s +2h)
A = (16 ft)(16 ft + 2×17 ft) = (16 ft)(50 ft)
A = 800 ft²
The total surface area is 800 square feet.
