Find the volume of the right triangular prism. The bases are equilateral triangles with a length of 6 mm. The height of the prism is 8.4 mm. (Round to the nearest tenth.)
V = Volume
A = Area of trangle
V = A * h
A = s ^ 2 * sqrt ( 3 ) / 4
where
s = length of equilateral triangle sides
A = 6 ^ 2 * sqrt ( 3 ) / 4
A = 36 * sqrt ( 3 ) / 4
A = 4 * 9 * sqrt ( 3 ) / 4
A = 9 * sqrt ( 3 )
A = 9 * 1.73025
A = 15.58845 mm ^ 2
V = A * h
V = 15.58845 * 8 .4
V = 130.94298 mm ^ 3
V = 130.9 mm ^ 3 rounded to the nearest tenth
very inteligent but also incorrect the answer is 23squared multiplied by pi
To find the volume of a right triangular prism, you need to multiply the area of the base by the height of the prism.
Step 1: Find the area of the base:
Since the base is an equilateral triangle, you can use the formula for the area of an equilateral triangle: A = (√3 / 4) * side^2, where side is the length of one side of the equilateral triangle.
Given that the length of each side is 6 mm, you can calculate the area of one equilateral triangle using the formula:
A = (√3 / 4) * 6^2
A = (√3 / 4) * 36
A = (√3 / 4) * 36
A = (√3 / 4) * 9 * 4
A = (√3 / 4) * (3^2) * 4
A = (√3 / 4) * 3^2 * 4
A = (√3 / 4) * 9 * 4
A = (√3 / 4) * 36
A ≈ 15.6 mm^2
Step 2: Calculate the volume of the prism:
To find the volume, multiply the area of the base by the height of the prism.
Volume = Area of base * Height
Volume = 15.6 mm^2 * 8.4 mm
Volume ≈ 131 mm^3
Therefore, the volume of the right triangular prism is approximately 131 mm^3.