Question

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

Answer 1

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
• $A = \sqrt{s(s-a)(s-b)(s-c)} =\sqrt{16*6*6*4} =48$

Total surface area is:

• 48*3 +  36√3 =
• 144 +  36√3

Correct choice is C