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?
Accepted Solution
A:
This question is incomplete. Find attached to this answer the required diagram.Answer:16√3 cm³Step-by-step explanation:Volume of a pyramid = 1/3 × Base area × HeightThe base area is given as 12√3 cm²But the height is not givenFrom the attached diagram an angle was givenUsing Trigonometric function of Tangenttan = Opposite/AdjacentOpposite = Height of the pyramidAdjacent = base length of the pyramid = 4√3Hence,tan 30° = opposite/4√3Cross multiplyOpposite = tan 30° × 4√3Opposite = Height of the pyramid = 4 cmVolume of a pyramid = 1/3 × Base area × Height= 1/3 × 12√3 × 4= 16√3 cm³