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With show work please. a and b.

With show work please. a and b.-example-1

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Explanation:

(a)

the sum of all internal angles in a polygon with n sides is

(n - 2)×180.

since in a regular polygon all angles are equally large, we get for one internal angle :

(n - 2)×180/n

for our hexagon this means the internal angle is

(6 - 2)×180/6 = 4×30 = 120°

(b)

the area of the hexagon is (as the graphic so nicely suggests) the sum of the areas of all 6 inner triangles.

the area of a triangle is

baseline × height / 2

baseline = 10 cm

the height (from the tip of the triangle down to the baseline in a right angle) is half of 17.3 cm, because these 17.3 cm are the sum of the 2 heights of 2 triangles placed tip to tip.

so, height = 17.3/2 = 8.65 cm

the area of one of the triangles is therefore

10 × 8.65 / 2 = 5 × 8.65 = 43.25 cm²

the total area of the hexagon is then

6 × 43.25 = 259.5 cm²

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