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In trapezium ABCD, AB//DC. M is mid poin...

In trapezium ABCD, AB//DC. M is mid point of AD and N is mid-point of BC.
If AB = 8 cm and DC = 11 cm , find MN.

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To find the length of MN in trapezium ABCD where AB is parallel to DC, we can use the properties of trapeziums and midpoints. Here’s a step-by-step solution: ### Step 1: Understand the trapezium and midpoints We have trapezium ABCD with AB || DC. M is the midpoint of AD, and N is the midpoint of BC. We are given: - AB = 8 cm - DC = 11 cm ### Step 2: Use the formula for the length of the line segment joining the midpoints of the non-parallel sides The length of the line segment joining the midpoints of the non-parallel sides (MN) in a trapezium can be calculated using the formula: \[ MN = \frac{AB + DC}{2} \] ### Step 3: Substitute the values into the formula Now, substituting the lengths of AB and DC into the formula: \[ MN = \frac{8 + 11}{2} \] ### Step 4: Calculate the sum Calculating the sum: \[ MN = \frac{19}{2} \] ### Step 5: Final calculation Now, performing the division: \[ MN = 9.5 \text{ cm} \] ### Conclusion Thus, the length of MN is 9.5 cm. ---
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