what's my Area?
Geometry
Level
pending
ABCDEF is a regular hexagon. One of its sides measures 6 inches. If O is the center of the hexagon, find the area of triangle AOB
12 square inches
18√3 square inches
18 square inches
9√3 square inches
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1 solution
There will be six equal triangles that can be formed with the vertex at the center of the hexagon. These triangles are equilateral as well and triangle AOB is one of these. Since the base AB or BA is 6 inches it also follows that OA and OB are as well 6 inches. Then the solution to find the area of this triangle follows which may vary depending on the knowledge of the solver. One could use special right triangle which I think is the easiest one. Heron's formula can also be used.
By construction, an altitude to the base AB can be drawn from O. This divides the triangle AOB to two equal special right triangles thus, finding the length of OA will just be a breeze. OA is therefore 3 square root of 3. Then multiply 3 square root of 3 by 3 that equals to 9 square root of 3. Or one can follow the formula in finding the area of a triangle which is half the product of the base and the altitude. that equals to half of 18 square root of 3 which is also 9 square root of 3.