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Please help me out :)-example-1
User El Sampsa
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Answer:

A = 25√3 cm²

Explanation:

View 5√3 cm as being the height of an equilateral triangle whose base is at the bottom of the purple figure. To find the area of one such triangle, we use the area-of-a-triangle formula A = (1/2)(b)(h).

opp

Using the sine function sin Ф = --------

hyp

we find the length of the hypotenuse, which is also the radius of the octagon, and because this is an equilateral triangle, is also the length of the base:

√3 5√3 cm

sin 60° = -------- = ------------- , which produces the value of hyp:

2 hyp

√3 5√3 cm

-------- = ------------- , which produces the value of hyp:

2 hyp

√3·hyp = 10√3, or hyp = 10 cm

Then the area of this one triangle is A = (1/2)(b)(h), or

A = (1/2) (10 cm)(5√3 cm) = 25√3 cm²

User Batty
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