KhaliqX431831 KhaliqX431831
  • 25-10-2022
  • Mathematics
contestada

the area of a trapezoid is given by the formula A= h(a+b)/2. solve for the formula for b.

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JouriX380117 JouriX380117
  • 25-10-2022

The formula is

[tex]A=\frac{(a+b)\cdot h}{2}[/tex]

To solve for b, first, we multiply the equation by 2

[tex]\begin{gathered} 2A=2\cdot\frac{(a+b)\cdot h}{2} \\ 2a=(a+b)\cdot h \end{gathered}[/tex]

Then, we divide the equation by h

[tex]\begin{gathered} \frac{2A}{h}=\frac{(a+b)h}{h} \\ \frac{2A}{h}=a+b \end{gathered}[/tex]

At last, we subtract a from each side

[tex]\frac{2A}{h}-a=a-a+b[/tex]

Hence, the final expression is

[tex]b=\frac{2A}{h}-a[/tex]

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