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150sqrt(3)-45 cubic feet
Let's consider the given composite solid.
We want to find the volume of this solid. First, let's find the area of its base B. To do this, we will subtract the area of the square from the area of the equilateral triangle.
We can find the area of the square by squaring its side length. A_(□)=(3 ft)^2 ⇔ A_(□)= 9 ft^2 To find the area of the triangle, we first need to find its height. To do so, we will consider the right triangle formed by one of the sides, the height, and half the base.
Substitute values
Calculate power
LHS-25=RHS-25
sqrt(LHS)=sqrt(RHS)
Split into factors
sqrt(a* b)=sqrt(a)*sqrt(b)
b= 10, h= 5sqrt(3)
1/b* a = a/b
Calculate quotient
Multiply
Base= 25sqrt(3)-9, height= 6
Distribute 6