Daily Regents: Literal Equations (August 2014)

I'll be reviewing a New York State Regents Exam Question every day from now until the Regents exams begin next month. At least, that is the plan.

August 2014, Questions 34

34. The formula for the area of a trapezoid is A = (1/2)h(b₁ + b₂).Express b₁ in terms of A, h, and b₂.

The area of a trapezoid is 60 square feet, its height is 6 ft, and one base is 12 ft. Find the number of feet in the other base.

You want to isolate the variable we want to solve for, in this case b₁:

A = (1/2)h(b₁ + b₂)
Multiply by 2: 2A = h(b₁ + b₂)
Divide by h: 2A/h = b₁ + b₂
Subtract b₂ from both sides: (2A/h) - b₂ = b₁
b₁ = (2A/h) - b₂

To find the answer to the second part, substitute the values you have into the equation you just created, and evaluate.

b₁ = (2A/h) - b₂ = (2(60)/6) - 12 = 120/6 - 12 = 20 - 12 = 8
The other base is 8 ft.

Any questions?

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