AMC 8 Daily Practice - Pythagorean Theorem

Complete problem set with solutions and individual problem pages

Problem 6 Easy

What is the area of square ABCD?

  • A.

    72

  • B.

    80

  • C.

    90

  • D.

    120

  • E.

    180

Answer:C

The area of a square can be calculated as \text{side length} \times \text{side length} or \frac{1}{2} \times \text{diagonal} \times \text{diagonal}.

Connect AC and draw CG \perp AE with G as the foot of the perpendicular.

Quadrilateral CFEG is a rectangle.

In \triangle ACG: AC^2 = AG^2 + CG^2 = 12^2 + 6^2 = 180.

Thus, the area of square ABCD is: \frac{1}{2} \times AC^2 = \frac{1}{2} \times 180 = 90.

Related Problems
Problem 4 AMC 8 Daily Practice - Pythagorean Theorem
Problem 5 AMC 8 Daily Practice - Pythagorean Theorem
Problem 7 AMC 8 Daily Practice - Pythagorean Theorem
Problem 8 AMC 8 Daily Practice - Pythagorean Theorem
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