The area of a trapezoid is given by the formula A = 1/2 (b 1 + b 2)h, where base b 1 is parallel to base b 2 and h is the height. Solve the formula for b 2. Show your work
b1+b2= 2*area/h
b2= above, minus b1
To solve the formula A = 1/2 (b1 + b2)h for b2, we'll follow these steps:
Step 1: Multiply both sides of the equation by 2 to remove the fraction:
2A = b1 + b2 * h
Step 2: Subtract b1 from both sides to isolate b2:
2A - b1 = b2 * h
Step 3: Divide both sides by h to solve for b2:
(b2 * h) = 2A - b1
b2 = (2A - b1) / h
Therefore, the formula for b2 is b2 = (2A - b1) / h.
To solve the formula A = (1/2)(b1 + b2)h for b2, we need to isolate b2 on one side of the equation.
Step 1: Start with the formula A = (1/2)(b1 + b2)h
Step 2: Multiply both sides of the equation by 2 to eliminate the fraction:
2A = (b1 + b2)h
Step 3: Distribute the h:
2A = b1h + b2h
Step 4: Subtract b1h from both sides of the equation:
2A - b1h = b2h
Step 5: Move b2h to the left side of the equation by subtracting b2h from both sides:
2A - b1h - b2h = 0
Step 6: Combine like terms:
2A - (b1h + b2h) = 0
2A - (b1 + b2)h = 0
Step 7: Factor out h:
2A - h(b1 + b2) = 0
Step 8: Move -h(b1 + b2) to the right side of the equation by adding it to both sides:
2A = h(b1 + b2)
2A/h = b1 + b2
Step 9: Subtract b1 from both sides:
2A/h - b1 = b2
b2 = 2A/h - b1
Therefore, the solution for b2 is b2 = 2A/h - b1.