The right triangular prism has bases that are equilateral triangles. The height is 8 in and the side of the base is 5 in , what is the prism's volume?
area = area of base x heigh
so the hard part is to find the area of the equilateral triangle with sides 5
1. easiest way:
area = (1/2) side^2 x sin60 = (1/2)(25)*√3/2
= 25√3
2. draw in the height of the triangle, call it h
h/5 = sin60
h = 5sin60
area = (1/2)(base x height)
= (1/2)(5)(5√3/2) = 25√3
(same as abov)
volume of prism = 25√3(8) = 200√3 cubic inches
thanks for the help
To find the volume of a right triangular prism, we can use the formula:
Volume = Area of the base × height
Since the base of the prism is an equilateral triangle, we can find the area of the base by first finding the length of the altitude of the equilateral triangle.
The altitude of an equilateral triangle can be found using the formula:
Altitude = (√3 / 2) × side length
Given that the side length of the equilateral triangle base is 5 inches, we can calculate the altitude:
Altitude = (√3 / 2) × 5 = (1.732 / 2) × 5 = 8.66 inches
Now that we know the height, h = 8 inches, and the length of the altitude of the base, A = 8.66 inches, we can calculate the area of the base:
Area of the base = (1/2) × base × height
= (1/2) × 5 × 8.66
= 21.65 square inches (rounded to two decimal places)
Finally, we can calculate the volume of the prism:
Volume = Area of the base × height
= 21.65 square inches × 8 inches
= 173.2 cubic inches (rounded to one decimal place)
Therefore, the volume of the right triangular prism is approximately 173.2 cubic inches.
To find the volume of a right triangular prism, we need to multiply the area of the base by the height.
Step 1: Find the area of the base
Since the base is an equilateral triangle, we need to find the area of an equilateral triangle with side length 5 inches.
The formula to find the area of an equilateral triangle is:
Area = (sqrt(3) / 4) * side length^2
Plugging in the value for the side length:
Area = (sqrt(3) / 4) * 5^2
Calculating:
Area = (sqrt(3) / 4) * 25
Area = (1.732 / 4) * 25
Area = 1.732 * 25 / 4
Area = 43.30 square inches (rounded to two decimal places)
Step 2: Multiply the area of the base by the height
The height of the prism is given as 8 inches.
Volume = Area of base * Height
Volume = 43.30 square inches * 8 inches
Volume = 346.40 cubic inches
Therefore, the volume of the right triangular prism is 346.40 cubic inches.