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Let two 8 × 12 rectangles share a common corner and overlap. The distance from the bottom right corner of one rectangle to the intersection point along the right edge of that rectangle is 7. What is the area of the shaded region?
  • a)
    36
  • b)
    45
  • c)
    48
  • d)
    54
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Let two 8 × 12 rectangles share a common corner and overlap. The dist...
Name the points as shown.
BE = BC - EC = 8 - 7 = 1
Applying the Pythagoras theorem to the right triangles ABE and AFE,
AE2 = AB2 + BE2 = 122 + 12 = 145
⇒ Area of ABEF = 6 + 36 = 42
⇒ Area of AFECD = Area of ABCD - Area of ABEF = (8 × 12) − 42 = 54
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