The half-sum of the bases of the trapeziums is 6 and the base difference is 4. Find the larger base.

Given a trapezoid ABCD, AD is a larger base, BC is a smaller base. By condition given: (AD + BC) / 2 = 6 cm; AD – BC = 4 cm. We get the system of equations. In the second equation, we express AD in terms of BC: AD = 4 + BC. Substitute the value AD into the first equation: (4 + BC + BC) / 2 = 6. Solve the resulting equation: (4 + 2BC) / 2 = 6. Using the basic property of the “cross to cross” proportion we get: 4 + 2BC = 12; 2BC = 8; BC = 8/2 = 4 (cm) Now, knowing the smaller base BC, we substitute this value into the second equation of the system of equations given by the condition, and find the larger base of the trapezoid AD: AD – BC = 4; AD – 4 = 4; AD = 4 + 4 = 8 (cm).
Answer: AD = 8 cm