What is the area of the overlapping region?
Consider the following for the next two (02) items that follow: Consider two identical rectangles ABCD and BEDF as shown in the figure given below. Let AB=1 cm and BC=2 cm.
- A. \frac{8}{5} square cm
- B. \frac{5}{4} square cm ✓
- C. \frac{4}{5} square cm
- D. \frac{3}{4} square cm
Correct Answer: B. \frac{5}{4} square cm
Explanation
The overlapping region of the two identical intersecting rectangles forms a rhombus. Let the side of this rhombus be x. In the right-angled triangle formed at the corner, the hypotenuse is x, and the legs are 1 and (2-x). Using the Pythagorean theorem: x^2 = 1^2 + (2-x)^2 \implies x^2 = 1 + 4 - 4x + x^2 \implies 4x = 5 \implies x = 5/4. The area of the rhombus is base \times height = (5/4) \times 1 = 5/4 square cm.
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