SOLUTION: How many inches long is the altitude of a regular triangular pyramid the base is 12 inches on a side and its volume is 103.8 cubic inches. Round off the answer to the nearest integ
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Question 1198257: How many inches long is the altitude of a regular triangular pyramid the base is 12 inches on a side and its volume is 103.8 cubic inches. Round off the answer to the nearest integer.
Answer by onyulee(41) (Show Source): You can put this solution on YOUR website!
**1. Find the Area of the Base**
* The base is an equilateral triangle with side length 12 inches.
* Area of an equilateral triangle = (√3/4) * side²
* Area of the base = (√3/4) * 12² = 36√3 square inches
**2. Use the Volume Formula**
* Volume of a pyramid = (1/3) * Base Area * Height
* 103.8 = (1/3) * 36√3 * Height
* Height = (103.8 * 3) / (36√3)
* Height ≈ 5 inches
**Therefore, the altitude of the regular triangular pyramid is approximately 5 inches.**
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