what is the perimeter of a hexagon with an apothem of 10

Assuming that said hexagon is regular then triangles formed (split in half by the apothem) are 30-60-90 triangles. The side that you'd get would be 10√3/3. Multiplied by two, you'd get 20√3/3. The perimeter would be 120√3/3, which would be 40√3 as the answer.

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maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-06-13T09:39:54+02:00

The perimeter of the hexagon is 40√3 if the apothem is 10 after applying tan ratio.

What is hexagon?

A hexagon is a six-sided polygon with six inner angles totalling 720° and six outside angles totalling 360° in geometry. Regular, irregular, concave, convex, and complicated hexagons are two-dimensional shapes.

From the figure, we can calculate the side length of the hexagon:

We know each interior angle of the hexagons = 120 degree

Half of the angle = 120/2 = 60 degree

From the tan ratio:

tan30 = (s/2)/10

1/√3 = s/20

s = 20/√3

Perimeter = 6×(20/√3) = 120/√3 = 40√3

Thus, the perimeter of the hexagon is 40√3 if the apothem is 10 after applying tan ratio.

Learn more about the hexagon here:

brainly.com/question/3295271

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