Answer:
A = 25√3 cm²
Step-by-step 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
