BTGmoderatorDC wrote: ↑Sun Jan 26, 2020 10:17 pm
A pyramid with four equal-sized flat surfaces and a base of 36 ft2 has a height of 10 feet. What is the total surface area of the pyramid, excluding the base?
A. 12 31^1/2
B. 12 109^1/2
C. 24 31^1/2
D. 24 109^1/2
E. 48 31^1/2
OA
B
Source: Veritas Prep
Since the pyramid has four equal-sized flat surfaces, the base must be a square; given that the area of the base is 36 sq feet, the side of the square = √36 = 6 ft.
Note that each of the four equal-sized flat surfaces would be like an isosceles triangle, whose base is 6 ft. We must get the height of the flat surfaces to get their area. To get the height, we must first get the height of the pyramid.
Drop a perpendicular from the tip of the pyramid to its base; from the point where the perpendicular touches the base, drop another perpendicular to one of the sides of the base. It is given that the height of the pyramid = 10 ft; since the side of the base = 6 ft, the length of the perpendicular to the side the base = 6/2 = 3 ft
Thus, this construction forms a rightangled triangle, whose height = 10 ft and base = 3 ft and hypotenuse = height of the flat surface of the pyramid = √(10^2 + 3^2) = √109
Thus, the area of the flat surface = 1/2*height*base = 1/2*√109*6 = 3*√109
Thus, the area of four equal-sized flat surfaces = 4*3*√109 = 12 √109 sq ft
The correct answer:
B
Hope this helps!
-Jay
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