Question
Find the long base $ a $ of a trapezoid if short base $b = 11\, \text{cm}$, height $h = 8\, \text{cm}$ and area $A = 136\, \text{cm}$.
Answer
$23$
Explanation
To find long base $ a $ use formula:
$$ A = \frac{ (a + b) \cdot h}{ 2 }$$After substituting $ A = 136 $ , $ b = 11 $ and $ h = 8 $ we have:
$$ 136\, \text{cm} = \frac{ (a + 11\, \text{cm}) \cdot 8\, \text{cm}}{ 2 }$$$$ 136\, \text{cm} \cdot 2 = (a + 11\, \text{cm}) \cdot 8\, \text{cm} $$$$ 272\, \text{cm} = (a + 11\, \text{cm}) \cdot 8\, \text{cm} $$$$ a + 11\, \text{cm} = \frac{ 272\, \text{cm} }{ 8\, \text{cm} } $$$$ a + 11\, \text{cm} = 34 $$$$ a = 34 - 11\, \text{cm} $$$$ a = 23 $$This page was created using
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