What is the area of triangle EOF?
Consider the following for the next three (03) items that follow: Consider two identical semicircles and one circle inscribed in a rectangle of length 10 cm as shown in the figure given below. (Take \pi=3.14 and \sqrt{2}=1.4).
- A. 12.5\sqrt{3} square cm
- B. 6.25\sqrt{3} square cm
- C. 12.5 square cm
- D. 6.25 square cm ✓
Correct Answer: D. 6.25 square cm
Explanation
Let E and F be the centers of the semicircles on the base. They completely fill the 10 cm length, so their radii are 2.5 cm, and EF = 5. The use of \sqrt{2}=1.4 implies a 45^{\circ}-45^{\circ}-90^{\circ} triangle relation for the centers. If OE = OF = 2.5\sqrt{2}, then the height of O above EF is 2.5. The area of \Delta EOF is \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 2.5 = 6.25 square cm.
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