As a landscaping project manager, you are determining the dimensions of a trapezoidal garden plot. You already know the total area ($A$), the height ($h$), and the length of the bottom base ($B$). To find the required length for the top base ($b$), you need to solve the trapezoid area formula, $A = \frac{1}{2} h(b + B)$, for $b$. Arrange the algebraic steps below in the correct order to recall the procedure for isolating $b$.

An urban planner is designing a trapezoidal park and needs to determine the length of the shorter base ($b$). The available data includes the total area ($A$), the height ($h$), and the length of the longer base ($B$). Which of the following equations represents the trapezoid area formula, $A = \frac{1}{2}h(b+B)$, correctly solved for $b$?

A sheet metal fabricator is using the area formula, $A = \frac{1}{2}h(b + B)$, to determine the length of the shorter base ($b$) for a custom trapezoidal vent. To solve the formula for $b$, the fabricator follows a sequence of inverse algebraic operations. Match each operation with its primary purpose in the isolation process.

Isolating Base b in the Trapezoid Area Formula

A manufacturing technician uses the formula $A = \frac{1}{2}h(b + B)$ to calculate the area of a trapezoidal component. When solving for the top base ($b$), the technician first clears the fraction and divides by the height, resulting in the intermediate equation $\frac{2A}{h} = b + B$. To finish isolating $b$, the technician must subtract the variable ____ from both sides of the equation.

A residential landscaper is estimating the materials needed for a trapezoidal backyard patio. To find the length of the shorter parallel side ($b$), the landscaper begins with the standard area formula $A = \frac{1}{2}h(b + B)$. If the landscaper knows the total area ($A$), the height ($h$), and the length of the longer parallel side ($B$), the correct equation solved for the shorter base is $b = \frac{2A}{h} - B$.

Standardizing Trapezoidal Part Calculations in Manufacturing