If the arc of a circle measures 38° and has an arc length of 4π cm,?
then find the area of the square inscribed in the circle to the nearest whole number.
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then find the area of the square inscribed in the circle to the nearest whole number.
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Use proportions to find the circumference C of the circle.
4 pi / 38 = C / 360
C = 360 ( 4 pi ) / 38
C = 720 pi / 19
C = 2 pi R
=> 2 pi R = 720 pi / 19
R = 720 / (19 * 2 )
R = 360 / 19
Draw the circle with the square incribed in it. Draw a diagonal in the square. Label the length of the diagonal 2R. Label the sides of the square x.
sin 45 = x / (2R)
( sqrt (2) ) / 2 = x / ( 2 R )
x = R sqrt (2)
The area of the squre is
A = x^2 = 2 R^2
= 2 ( 360 / 19 )^2
Answer: 718 cm^2