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The area of a trapezoid is calculated using the formula below, where [tex]$A$[/tex] is the area of the trapezoid, [tex]$b_1$[/tex] and [tex]$b_2$[/tex] are the bases of the trapezoid, and [tex]$h$[/tex] is the height of the trapezoid.
[tex]$A=\frac{b_1+b_2}{2} \cdot h$[/tex]
Rewrite the formula to find the base [tex]$b_2$[/tex].
Answer (2)
Multiply both sides of the equation by 2: 2 A = ( b 1 + b 2 ) h .
Divide both sides of the equation by h : h 2 A = b 1 + b 2 .
Subtract b 1 from both sides: h 2 A − b 1 = b 2 .
Rewrite the equation to express b 2 : b 2 = h 2 A − b 1 .
Explanation
Understanding the Formula We are given the formula for the area of a trapezoid: A = 2 b 1 + b 2 ". h , where A is the area, b 1 and b 2 are the lengths of the bases, and h is the height. Our goal is to isolate b 2 on one side of the equation.
Multiply by 2 First, let's multiply both sides of the equation by 2 to get rid of the fraction: 2 A = ( b 1 + b 2 ) h
Divide by h Next, we divide both sides by h to isolate the term ( b 1 + b 2 ) : h 2 A = b 1 + b 2
Subtract b_1 Now, subtract b 1 from both sides to solve for b 2 : h 2 A − b 1 = b 2
Final Answer Finally, we can rewrite the equation with b 2 on the left side: b 2 = h 2 A − b 1
Examples
Understanding how to rearrange formulas like the area of a trapezoid is useful in many real-world scenarios. For example, if you're designing a garden bed in the shape of a trapezoid and you know the area you want it to cover, the length of one base, and the desired height, you can use this rearranged formula to determine the length of the other base. This ensures your garden bed fits perfectly in your available space and meets your desired area.
To find the base b 2 of a trapezoid using the area formula, first multiply the equation by 2, divide by the height, and then subtract b 1 . The rearranged formula is b 2 = h 2 A − b 1 . This helps in calculating the unknown base when the area, height, and one base are known.
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