Question

Given: Regular pyramid DO = 6, m ADO : 42°, AO Perpendicular (FBCD) Find: V and Surface Area Of ABCDF

Answer 1

the height of pyramid

tan 42°=h/ DO

h=6 tan 42° = 5.4 units

the side of base a = 2DO/√2 = √2DO = 6√2 = 8.5 units

volume= V = a?h/3 = 8.52(5.4)/3 = 130.1 units

surface area{S }= a + 4×1/2×a/(a/2)² + h² =

8.5²+ 2*8.5 √((8.5/2)² + 5.4²)= 189.7 unit²

Answer 2

Assumed the base is a square

Find the height:

• h / DO = tan 42°
• h = 6 tan 42° ≈ 5.4 units

Find the side of base:

• a = 2DO/√2 = √2DO = 6√2 ≈ 8.5 units

Find volume:

• V = a²h/3 = 8.5²(5.4)/3 ≈ 130.1 units³

Find the surface area:

• S = a² + 4*1/2*a
  `√((a/2)^2+h^2)` = 8.5² + 2*8.5
  `√((8.5/2)^2+5.4^2)` ≈ 189.7 units²