anmolmakkarz17 wrote:
In the figure above, ABCDEF is a regular hexagon with vertices A and C on the circle centered at point B. Is the perimeter of the figure greater than 40 ?
1) The overlapping region between circle B and hexagon ABCDEF has an area of 12π.
2) The area of the figure is 24\(\pi\) +54 \(\sqrt{3}\)
B is the centre of the circle and the vertex of a regular hexagon. So angle ABC will be 120 degrees.
This means sector ABC will be 1/3rd the area of the triangle. The radius BC (or BA) is also the side of the hexagon. If we know its measure, we will know the area of the circle as well as the area of the hexagon.
Also, the regular hexagon is made up of 6 equal equilateral triangles. So if we know the area of the hexagon, we know the area of each triangle and the measure of each side of the hexagon.
Ques: Is the perimeter of the figure greater than 40 ?
If we know the measure of the side of the figure, we will know whether its perimeter will be greater than 40. So what we need is the measure of the side of the hexagon.
1) The overlapping region between circle B and hexagon ABCDEF has an area of 12π.
This tells us that area of the sector is 12π. This is 1/3rd the area of the circle so we can find the area of the circle. Then we can find the radius of the circle which is same as side of the hexagon. Sufficient alone.
2) The area of the figure is 24
This is the area of the figure which is 6 times the area of each equilateral triangle. So we can find the area of each equilateral triangle which will give us the measure of each side of hexagon.
Sufficient alone
Answer (D)
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Karishma
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