Find the lateral area the regular pyramid. (50 points)
L. A. =
having trouble with these PLEASE HELP :)
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Answer:
The lateral area the regular pyramid = 18√91 square units
Step-by-step explanation:
It is given a regular hexagon.
From the figure we get the base edge of the pyramid is 6 units
(Since the base of pyramid is regular hexagon
To find the lateral edge
Lateral edge is the hypotenuse of triangle with base = 6 and height = 8
Lateral edge =√(8² + 6²) = √100 = 10
To find the slant height
Slant height is the height of triangle with,
base = 6/2 = 3 and hypotenuse = 10
Slant height = √(10² - 3²) = √(100 - 9) = √91
To find the area of single face
Area = bh/2
b = 6 and h = √91
Area = (6 * √91)/2 = 3√91
To find the lateral area of pyramid
Lateral area = 6*face area = 6*3√91 = 18√91 square units