Question

PLEASE HELP

Find the surface area of the composite solid if the base is a regular hexagon. Round your answer to the nearest hundredth.
A.
471.53 m2
B.
615.53 m2
C.
709.06 m2
D.
802.59 m2

Answer 1

b.

Explanation:

Answer 2

The answer is B. 615.53 m2.

The surface area (SA) is the sum of base area (A1), 6 areas of rectangle with sides 6 m and 7m (A2), and 6 areas of triangles with sides 15 m and 6 m (A3):
SA = A1 + 6A2 + 6A3
____
A1 = 3√3 * a² / 2
a = 6 m
A1 = 3√3 * 6² / 2 = 3√3 * 36 / 2 = 54√3 = 93.53 m²
____
A2 = a * b
a = 6 m
b = 7 m
A2 = 6 * 7 = 42 m²
____
A3 = a * h / 2
a = 6 m
h = 15 m
A3 = 6 * 15 / 2 = 45 m²
__________

SA = A1 + 6A2 + 6A3
SA = 93.53 + 6 * 42 + 6 * 45 = 93.53 + 252 + 270 = 615.53 m²