Question

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

Answer 1

• C. 144 + 36√3

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
• 
  `A = √(s(s-a)(s-b)(s-c)) =√(16*6*6*4) =48`

Total surface area is:

• 48*3 + 36√3 =
• 144 + 36√3

Correct choice is C