Question 113

Let PQRSTU be a regular hexagon. The ratio of the area of the triangle PRT to that of the hexagon PQRSTU is

Solution

It's given that PQRSTU is a regular hexagon and O is the center of the hexagon.

If we fold $$\triangle$$TSR ,$$\triangle$$PQR ,$$\triangle$$TUP along lines TR, PR, PT respectively then vertices S,Q,U will overlap each other exactly at center of the hexagon.

Hence we can say that Area of hexagon PQRSTU = 2($$\triangle$$PRT)

So Area of $$\triangle$$PRT = 0.5(Area of hexagon PQRSTU)

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