The perimeter of the base of the pyramid is 66 feet. 18 feet is the length of one side of the base. the sides are not parallel What is the length of the missing side of the base? the height is 78 What is the volume of the pyramid?
To find the length of the missing side of the base, we first need to determine the total perimeter of the base. Since one side is 18 feet, and there are four sides in total, the perimeter is 66 feet.
Therefore, the total length of the other three sides is 66 - 18 = 48 feet.
Since the sides are not parallel, we cannot assume that the remaining sides are all equal in length.
Let x be the length of the missing side of the base.
So the total length of the three equal sides is 2x, and the length of the remaining side is x.
From this, we can form the equation:
2x + x = 48
3x = 48
x = 16 feet
Therefore, the missing side of the base is 16 feet.
To find the volume of the pyramid, we can use the formula:
Volume = (1/3) x Base Area x Height
Since the base is a triangle, we can calculate the area using the formula for the area of a triangle:
Area of base = (1/2) x base x height = (1/2) x 18 x 16 = 144 square feet
Plugging in the values, we get:
Volume = (1/3) x 144 x 78 = 3744 cubic feet
Therefore, the volume of the pyramid is 3744 cubic feet.