AMC 8 Daily Practice Round 6

Complete problem set with solutions and individual problem pages

Problem 29 Easy

Two squares with sides a and b satisfy a+b=10 and ab=20.Find the shaded area.

  • A.

    20

  • B.

    30

  • C.

    40

  • D.

    45

  • E.

    60

Answer:B

Shaded area

A = \frac{1}{2}a^2 + \frac{1}{2}b(a+b) - \frac{1}{2}ab = \frac{1}{2}(a^2 + b^2).

From (a+b)^2 = a^2 + 2ab + b^2 = 100 \implies a^2 + b^2 = 100 - 40 = 60

Therefore A = \frac{1}{2} \times 60 = 30

Final result: \boxed{30}

Related Problems
Problem 26 AMC 8 Daily Practice Round 6
Problem 27 AMC 8 Daily Practice Round 6
Problem 28 AMC 8 Daily Practice Round 6
Problem 30 AMC 8 Daily Practice Round 6
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