Question

A solid oblique pyramid has an equilateral triangle as a base with an edge length of 4StartRoot 3 EndRoot cm and an area of 12StartRoot 3 EndRoot cm2.
What is the volume of the pyramid?

Answer 1

The volume of the pyramid is $16\sqrt{3}$ cm³ ⇒ 2nd answer

Step-by-step explanation:

The volume of a pyramid = $\frac{1}{3}$ base area × its height

The given is:

1. The base of the pyramid is an equilateral triangle of side length

   $4\sqrt{3}$ cm

2. The area of the base is $12\sqrt{3}$ cm²

3. In Δ ACB measure of angle ACB is 90° and m∠ CAB is 30°

To find the volume of the pyramid we need its height

∵ The height of the pyramid is BC

- Because it is perpendicular to the side AC which is one side of the

  base of the pyramid

∵ m∠CAB = 30°

∵ AC = $4\sqrt{3}$ cm

- By using tan(30) = $\frac{BC}{AC}$ we can find BC

∴ tan(30) = $\frac{BC}{4\sqrt{3}}$

- By using cross multiplication

∴ BC = $4\sqrt{3}*tan(30)$

∴ BC = 4 cm

∵ V = $\frac{1}{3}$ area of the base × BC

∵ BC = 4 cm

∵ The area of the base is $12\sqrt{3}$

∴ V = $\frac{1}{3}$ × $12\sqrt{3}$ × 4

∴ V = $16\sqrt{3}$ cm³

The volume of the pyramid is $16\sqrt{3}$ cm³

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Answer 2

Answer:

b

Step-by-step explanation:

i did the test