Official Guide Explanation:
Problem Solving #71




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Solution and Metadata

Question: 71
Page: 71
Difficulty: 5 (Moderate)
Category 1: Geometry > Triangles > Multiple figures
Category 2: Geometry > Triangles > Special Tris
Category 3: Geometry > Triangles > Pythag

Explanation: To find the area of BCD, we need the base and the height--two dimensions of the triangle that are perpendicular. Since BCD is a right triangle, those are two sides: BC and BD. We're given BC = 4, so we need BD.

BD is the hypotenuse of BAD, and we know the two other sides of BAD. Since the two legs are equal, it is a 45:45:90 triangle, meaning that the hypotenuse is rt[2] times greater than the length of each leg. Thus, BD = 4 rt[2].

Now we can solve for area: (1/2)bh = (1/2)(4 rt[2])(4) = 8 rt[2], choice (C).

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