Question
2 If the lengths of the two parallel bases of a trapezium are \( 15 \mathrm{~cm} ., 11 \mathrm{~cm} \)., then the length of its middle base is \( \ldots \ldots \ldots \ldots . . . \mathrm{cm} \). \( \begin{array}{llll}\text { (a) } 4 & \text { (b) } 26 & \text { (c) } 13 & \text { (d) } 12\end{array} \)
Ask by Sherman Washington. in Egypt
Mar 11,2025
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Tutor-Verified Answer
Answer
The length of the middle base is 13 cm.
Solution
1. Let the lengths of the two parallel bases be \( a = 15 \, \text{cm} \) and \( b = 11 \, \text{cm} \).
2. The length of the middle base (also known as the midline) of a trapezium is calculated by taking the average of the two bases. The formula is:
\[
M = \frac{a+b}{2}
\]
3. Substituting the given values:
\[
M = \frac{15 + 11}{2} = \frac{26}{2} = 13 \, \text{cm}
\]
Thus, the length of the middle base is \( 13 \, \text{cm} \).
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Simplify this solution Beyond the Answer
To find the length of the middle base of a trapezium with parallel bases of \( 15 \, \text{cm} \) and \( 11 \, \text{cm} \), you can use the average of the two bases: \[ \text{Middle Base} = \frac{\text{Base}_1 + \text{Base}_2}{2} = \frac{15 \, \text{cm} + 11 \, \text{cm}}{2} = \frac{26 \, \text{cm}}{2} = 13 \, \text{cm}. \] So the answer is \( \text{(c) } 13 \, \text{cm} \). When dealing with trapeziums, a common mistake is to confuse the middle base with the height. Remember, the middle base is simply the average of the lengths of the two parallel sides. It's easy to overlook that the bases can have different lengths while still forming a trapezium!
