Question

Find the total area for the regular pyramid.

• 280 + 54^3 sq. units
• 18^91 + 54^3 sq. units
• 360 + 54^3 sq. units
• 360^3 sq. units

Answer 1

• Option B

Explanation:

Given is the hexagonal pyramid.

We know the radius of the base is same as its side.

Find the base area:

• A = 3√3/2a²
• A = 3√3/2*6² = 54√3

Given the height and radius, find the side of the lateral triangular faces:

• 
  `√(8^2+6^2) =√(100) =10`

Each of 6 triangles have sides 10, 10 and 6 units.

Find the area using heron's formula:

• s = P/2 = (10*2 + 6)/2 = 13
• s - a = s - b = 13 - 10 = 3
• s - c = 13 - 6 = 7
• 
  `A = √(s(s-a)(s-b)(s-c)) =√(13*3*3*7) =3√(91)`

Total surface area:

• 
  `S = 6*3√(91)+54√(3) =18√(91)+54√(3)`

Correct choice is B