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

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

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)

Answer 2

(A) and (D)

Explanation:

It is given that the given expression
`a=(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=(1)/(2)(b_(1)+b_(2))h`

`(2a)/(h)-b_(2)=b_(1)`

And the expression for height is:

`2a=(b_(1)+b_(2))h`

`h=(2a)/((b_(1)+b_(2)))`

(A) The given expression is:

`(2a)/(h)-b_(2)=b_(1)`

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

(B) The given expression is:

`(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:

`(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:

`(2a)/(b_(1)+b_(2))=h`

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

(E) The given expression is:

`(a)/(2(b_(1)+b_(2)))=h`

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