The half-sum of the bases of the trapeziums is 10 and the difference is 6 find the smaller base.

Given a trapezoid ABCD, AD is a larger base, BC is a smaller base. Given the condition: (AD + BC) / 2 = 10 cm; AD – BC = 6 cm. We get the system of equations. In the second equation, we express AD in terms of BC: AD = 6 + BC. Substitute the AD value into the first equation: (6 + BC + BC) / 2 = 10. Solve the resulting equation: (6 + 2BC) / 2 = 10. Using the basic property of the cross-to-cross proportion, we get: 6 + 2BC = 20; 2BC = 20 – 6; 2BC = 14; BC = 14/2 = 7 (cm). Answer: BC = 7 cm.