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Find the total area for the pyramid with the equilateral base.



• 12 +36v3 sq. units
• 36 + 144V3 sq. units
• 144 +36V3 sq. units
• 36 +12V3 sq units

Find the total area for the pyramid with the equilateral base 12 36v3 sq units 36 144V3 sq units 144 36V3 sq units 36 12V3 sq units class=

Respuesta :

mhanifa

Answer:

  • C. 144 +  36√3

Step-by-step explanation:

Area formula for equilateral triangle with side a:

  • A = √3/4a²

The base area is:

  • A = √3/4*12² = 36√3

The three lateral surfaces have same sides of 10, 10 and 12.

Find each surface area using heron's formula:

  • s = P/2 = (10 + 10 + 12)/2 = 16
  • s - a = 16 - 10 = 6
  • s - b = 6
  • s - c = 16 - 12 = 4
  • [tex]A = \sqrt{s(s-a)(s-b)(s-c)} =\sqrt{16*6*6*4} =48[/tex]

Total surface area is:

  • 48*3 +  36√3 =
  • 144 +  36√3

Correct choice is C

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