A solid oblique pyramid has an equilateral triangle as a base with an edge length of 4StartRoot 3 EndRoot cm and an area of 12St
artRoot 3 EndRoot cm2. What is the volume of the pyramid?
1 answer:
This question is incomplete. Find attached to this answer the required diagram.
Answer:
16√3 cm³
Step-by-step explanation:
Volume of a pyramid = 1/3 × Base area × Height
The base area is given as 12√3 cm²
But the height is not given
From the attached diagram an angle was given
Using Trigonometric function of Tangent
tan = Opposite/Adjacent
Opposite = Height of the pyramid
Adjacent = base length of the pyramid = 4√3
Hence,
tan 30° = opposite/4√3
Cross multiply
Opposite = tan 30° × 4√3
Opposite = Height of the pyramid = 4 cm
Volume of a pyramid = 1/3 × Base area × Height
= 1/3 × 12√3 × 4
= 16√3 cm³
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