Answer:
The lateral area the regular pyramid = 18√91 square units
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