Answer:
[tex]Volume=\frac{16\sqrt{2} }{3}units^{3}[/tex]
Step-by-step explanation:
∵ The volume of the pyramid = 1/3 base area × height
∵ The base is equilateral Δ with side length 4
∴ The area of the bast = 1/4 × 4² × √3 = 4√3 units²
To get the height of the pyramid draw it from the vertex of the top of the pyramid ⊥ to the base on the centro-id of the base which divides the height of the triangle two ratio 2:1 from the vertex of the triangle
∵ The height of the base = √(4² - 2²) =√12 = 2√3
∴ 2/3 the height = 4√3/3 ⇒ (2:1 means 2/3 from the height)
∴ The height of the pyramid = √[4² - (4√3/3)²] = √[16 - 48/9]
∴ h = 4√2/√3 (4√6/3 in its simplest form)
∴ V = 1/3 × 4√3 × 4√2/√3 = 16√2/3 units³
∴ [tex]V = \frac{16\sqrt{2} }{3}[/tex]
