Question

the equation a=1/2(b1+b2)h can be used to determine the area, a, of a trapezoid with height, h, and base lengths, b1 and b2. which are equivalent equations? check all that apply.

Answer 1

Answer:

(A) and (D)

Step-by-step explanation:

It is given that the given expression $a=\frac{1}{2}(b_{1}+b_{2})h$can be used to determine the area, a, of a trapezoid with height, h, and base lengths $b_{1}$ and $b_{1}$.

Thus, solving the given equation and finding the value of $b_{1}$, we get

$a=\frac{1}{2}(b_{1}+b_{2})h$

$\frac{2a}{h}-b_{2}=b_{1}$

And the expression for height is:

$2a=(b_{1}+b_{2})h$

$h=\frac{2a}{(b_{1}+b_{2})}$

(A) The given expression is:

$\frac{2a}{h}-b_{2}=b_{1}$

which is equivalent to the given expression, therefore this option is correct.

(B) The given expression is:

$\frac{a}{2h}-b_{2}=b_{1}$

which is not equivalent to the given expression, therefore this option is not correct.

(C) The given expression is:

$\frac{2a-b_{2}}{h}=b_{1}$

which is not equivalent to the given expression, therefore this option is not correct.

(D) The given expression is:

$\frac{2a}{b_{1}+b_{2}}=h$

which is equivalent to the given expression, therefore this option is correct.

(E) The given expression is:

$\frac{a}{2(b_{1}+b_{2})}=h$

which is not equivalent to the given expression, therefore this option is not correct.

Answer 2

Answer:

b₁ = (2a – b₂h)/h; b₁ = (2a)/h – b₂; h = (2a)/(b₁ + b₂)

Step-by-step explanation:

A. Solve for b₁

          a = ½(b₁ + b₂)h        Multiply each side by 2

        2a = (b₁ + b₂)h           Remove parentheses

        2a = b₁h + b₂h           Subtract b₂h from each side

2a - b₂h = b₁h                    Divide each side by h

         b₁ = (2a – b₂h)/h     Remove parentheses

         b₁ = (2a)/h – b₂

B. Solve for h

2a = (b₁ + b₂)h     Divide each side by (b₁ + b₂)

 h = (2a)/(b₁ + b₂)