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What is the surface area of this square pyramid?

A. 4yd^2

B. 25.1yd^2

C. 36.7yd^2

D. 57.8yd^2

arota21  May 23, 2017
 #1
avatar+17746 
+2

The base is a square; therefore, its area is 4.62  =  21.16.

 

Since the left-hand triangle of the front sides is a 30-60-90 triangle, the dashed line segment has a value equal to

sqr(3) x the base of the left-hand triangle (the distance from the corner dot to the middle dot). Since the distance from the corner dot to the middle dot = 1/2 x 4.6 = 2.3, the length of the dashed line segment = 2.3 x sqrt(3).

The area of the front triangle = 1/2 x base x height = 1/2 x (4.6) x (2.3 x sqrt(3)) = 9.1625.

 

The total surface area = (area of the base) + 4 x (area of the front triangle) = 21.16 + 4 x (9.1625)  =  57.81 square yds.

geno3141  May 23, 2017

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