Select the correct answerIn the given figure ABC is a triangle in which CDEFG is a pentagon. Triangles ADE and BFG are equilateral triangles each with side 2 cm and EF=2 cm. Find the area of the Pentagon.radio_button_unchecked8√3 cmradio_button_unchecked7√3 cmradio_button_unchecked15√3 cmradio_button_unchecked11.28 cm
Question
Select the correct answerIn the given figure ABC is a triangle in which CDEFG is a pentagon. Triangles ADE and BFG are equilateral triangles each with side 2 cm and EF=2 cm. Find the area of the Pentagon.radio_button_unchecked8√3 cmradio_button_unchecked7√3 cmradio_button_unchecked15√3 cmradio_button_unchecked11.28 cm
Solution
To find the area of the pentagon CDEFG, we first need to find the areas of the two equilateral triangles ADE and BFG, and then add the area of the rectangle EF.
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The area of an equilateral triangle with side length 'a' is given by the formula: (sqrt(3)/4)*a^2. Here, the side length is 2 cm. So, the area of each equilateral triangle is (sqrt(3)/4)2^2 = sqrt(3) cm^2. Since there are two such triangles, their combined area is 2sqrt(3) cm^2.
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The rectangle EF has length EF = 2 cm and width DE = FG = 2 cm (since triangles ADE and BFG are equilateral). So, its area is 2*2 = 4 cm^2.
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Adding these areas together, the total area of the pentagon CDEFG is 2sqrt(3) cm^2 + 4 cm^2 = 2sqrt(3) + 4 cm^2.
None of the given options match this result. There might be a mistake in the question or the answer choices.
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