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Answers
Answer:
101.08 square cm
Step-by-step explanation:
In the given circle, the petals are formed by drawing circles curves of same radius.
Each curve is drawn by keeping center on perimeter of circle. Where the circles cuts the perimeter, we again draw circles.
Hence each petal is segment of the circle of same radius and the segment is formed by line whose length is equal to radius.
See the diagram 1. This segment is half of single peter in the given problem.
So to calculate the area of this segment, it makes an angle of 60° at center as shown in figure 2. (because all three sides are of length radius)
Area of Segment = ( θ × π/360 − sin(θ)/2 ) × r² (when θ is in degrees)
= (60* π/360 − sin(60)/2 ) × 7²
= (π/6 - √3)/4)*49
= (0.52 - 0.43)*49 = 4.41 square cm.
Area of petal = 2 * 4.41 = 8.82.
There are 6 such petals.
Hence petals area = 6 * 8.82 = 52.92 scm.
Area of circle = πr² = 22*7*7/7 = 154 scm
Area of the shared part = area of circle - area of petals
= 154 - 52.92 = 101.08 scm
Answer:
100.6 cmsq
Step-by-step explanation:
area of complete circle = pie r * r
=(22/7)*7*7 = 154 cmsq
6 petals are made of
12 arcs if we take arc from perimieter of circle to center of circle.
radius of arc of petal = 7cm
area of half petal = arc segment area - triangle area formed with two radius and straight line joining arc ends
triangle would be equilateral with side = 7 cm
area of triangle = (root3 /4) * 7*7 = 21.22 cmsq
area of arc segment = (60/360)* (22/7)*7*7 =25.67 cmsq
area of half petal = 25.67-21.22
= 4.45
area of 1 petal = 2*4.45 = 8.9
area of 6 petals = 8.9*6 = 53.4 cmsq
area of shaded region = area of circles - area of petals
= 154-53.4
= 100.6 cmsq