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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

Find The Total Area For The Regular Pyramid 280 543 Sq Units 1891 543 Sq Units 360 543 Sq Units 3603 Sq Units class=

Sagot :

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Answer:

  • Option B

Step-by-step 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:

  • [tex]\sqrt{8^2+6^2} =\sqrt{100} =10[/tex]

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
  • [tex]A = \sqrt{s(s-a)(s-b)(s-c)} =\sqrt{13*3*3*7} =3\sqrt{91}[/tex]

Total surface area:

  • [tex]S = 6*3\sqrt{91}+54\sqrt{3} =18\sqrt{91}+54\sqrt{3}[/tex]

Correct choice is B

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