Question

the function a(b) relates The area of a trapezoid with a given height of 12 and one base length of 9 with the length of its other base

Answer 1

Solving for b, we have the equation A(b)=12*(b+9)/2 - we cancel out 12 and the 1/2 to get 6(b+9)=A(b) and get 6b+54=A(b). Subtract 54 from both sides to get 6b=A(b)-54 and divide both sides by 6 to get b=A(b)/6-9 = A

Answer 2

The equation that represents the function B(a) as the length of the side parallel to the base is B(a) = a/6 - 9, as per the area of a trapezoid.

What is the area of a trapezoid?

If the length of two parallel sides of a trapezoid is 'a', 'b' and the height of that trapezoid is 'h', then the area of a trapezoid can be represented as

= [(a + b)h]/2

Given, the base of the trapezoid is 9 and the height of the trapezoid is 12.

Therefore, 'b' is the parallel side of the base.

The given function that represents the area of the trapezoid is:

A(b) = [12(b + 9)]/2

Let, A(b) = a.

Therefore, a =  [12(b + 9)]/2

⇒ 2a = 12(b + 9)

⇒ a = 6(b + 9)

⇒ a = 6b + 54

⇒ 6b = a - 54

⇒ b = (a - 54)/6

⇒ b = a/6 - 9

If we assume the length of the side parallel to the base 'b' = B(a), therefore, the equation will be:

B(a) = a/6 - 9

Learn more about the area of a trapezoid here: https://brainly.com/question/14310829

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