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A=(1)/(2)(b_(1)+b_(2))h
The area, 
A, of a trapezoid that has a height, 
h, and bases, 
b_(1) and 
b_(2), can be found by using the given equation. Which of the following correctly shows the trapezoid's height in terms of its area and 2 bases?
Choose 1 answer:
(A) 
h=(A)/(2)(b_(1)+b_(2))
(B) 
h=(2)/(A(b_(1)+b_(2)))
(c) 
h=(A)/(2(b_(1)+b_(2)))
(D) 
h=(2A)/((b_(1)+b_(2)))

A=12(b1+b2)h A=\frac{1}{2}\left(b_{1}+b_{2}\right) h \newlineThe area, A A , of a trapezoid that has a height, h h , and bases, b1 b_{1} and b2 b_{2} , can be found by using the given equation. Which of the following correctly shows the trapezoid's height in terms of its area and 22 bases?\newlineChoose 11 answer:\newline(A) h=A2(b1+b2) h=\frac{A}{2}\left(b_{1}+b_{2}\right) \newline(B) h=2A(b1+b2) h=\frac{2}{A\left(b_{1}+b_{2}\right)} \newline(C) h=A2(b1+b2) h=\frac{A}{2\left(b_{1}+b_{2}\right)} \newline(D) h=2A(b1+b2) h=\frac{2 A}{\left(b_{1}+b_{2}\right)}

Full solution

Q. A=12(b1+b2)h A=\frac{1}{2}\left(b_{1}+b_{2}\right) h \newlineThe area, A A , of a trapezoid that has a height, h h , and bases, b1 b_{1} and b2 b_{2} , can be found by using the given equation. Which of the following correctly shows the trapezoid's height in terms of its area and 22 bases?\newlineChoose 11 answer:\newline(A) h=A2(b1+b2) h=\frac{A}{2}\left(b_{1}+b_{2}\right) \newline(B) h=2A(b1+b2) h=\frac{2}{A\left(b_{1}+b_{2}\right)} \newline(C) h=A2(b1+b2) h=\frac{A}{2\left(b_{1}+b_{2}\right)} \newline(D) h=2A(b1+b2) h=\frac{2 A}{\left(b_{1}+b_{2}\right)}
  1. Given formula: We are given the formula for the area of a trapezoid: A=12(b1+b2)hA = \frac{1}{2}(b_1 + b_2)h. We need to solve for hh in terms of AA, b1b_1, and b2b_2.
  2. Multiplying both sides: First, we multiply both sides of the equation by 22 to get rid of the fraction on the right side. This gives us 2A=(b1+b2)h2A = (b_1 + b_2)h.
  3. Dividing to isolate hh: Next, we divide both sides of the equation by (b1+b2)(b_1 + b_2) to isolate hh. This gives us h=2Ab1+b2h = \frac{2A}{b_1 + b_2}.
  4. Checking options: We check the options given to see which one matches our derived formula for hh. The correct formula for hh is (2A)/(b1+b2)(2A) / (b_1 + b_2), which corresponds to option (D)(D).

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