ABCD trapezoid find AD if BC is 8 cm and MN 10, MN is the middle line of the trapezoid.

The cutting line of the trapezoid is equal to half the sum of the bases.
So МN = 1/2 (AD + BC)
Substitute the known values:
10 = 1/2 (BP + 8)
10 = 1 / 2AD + 4
1 / 2ad = 10-4
1 / 2ad = 6
AD = 6 ÷ 1/2
AD= 12



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