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Solving the formula A = rac{1}{2} h(b + B) for
To solve the trapezoid area formula A = rac{1}{2} h(b + B) for the base , use the following steps:
- Write the formula: A = rac{1}{2} h(b + B).
- Clear the fraction by multiplying both sides by : .
- Divide both sides by to isolate the expression within the parentheses: rac{2A}{h} = b + B.
- Subtract from both sides to isolate : b = rac{2A}{h} - B.
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Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
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As a landscaping project manager, you are determining the dimensions of a trapezoidal garden plot. You already know the total area (), the height (), and the length of the bottom base (). To find the required length for the top base (), you need to solve the trapezoid area formula, , for . Arrange the algebraic steps below in the correct order to recall the procedure for isolating .
An urban planner is designing a trapezoidal park and needs to determine the length of the shorter base (). The available data includes the total area (), the height (), and the length of the longer base (). Which of the following equations represents the trapezoid area formula, , correctly solved for ?
A sheet metal fabricator is using the area formula, , to determine the length of the shorter base () for a custom trapezoidal vent. To solve the formula for , 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 to calculate the area of a trapezoidal component. When solving for the top base (), the technician first clears the fraction and divides by the height, resulting in the intermediate equation . To finish isolating , the technician must subtract the variable ____ from both sides of the equation.