ABCD is a quadrilateral in which AB|| DC, and E and F are the mid points of the diagonals AC and BD, respectively. If AB = 12 cm, BC = 40 cm, DC = 30 cm, and AD = 45 cm, then what is the length ( in cm) of EF?
ABCD is a quadrilateral in which AB|| DC, and E and F are the mid points of the diagonals AC and BD, respectively. If AB = 12 cm, BC = 40 cm, DC = 30 cm, and AD = 45 cm, then what is the length ( in cm) of EF?
ABCD एक चतुर्भुज है जिसमें AB ∥ DC है, तथा E और F क्रमशः विकर्णों AC और BD के मध्यबिंदु हैं। यदि AB = 12 सेमी, BC = 40 सेमी, DC = 30 सेमी और AD = 45 सेमी हैं, तो EF की लंबाई (सेमी में) ज्ञात कीजिए।
Detailed Solution & Logic
9
In a trapezium (quadrilateral with $AB \parallel DC$), the segment joining the midpoints of the diagonals is given by:
$EF = \frac{1}{2} |AB - DC|$
Given:
$AB = 12$ cm, $DC = 30$ cm
$EF = \frac{1}{2} (30 - 12)$
$= \frac{1}{2} \times 18 = 9$ cm
✅ Final Answer: 9 cm
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