the sum of all areas of all sectors each of the radius 7 which is formed at sll vertecies of quadrilatera .
Answers
Given : sectors each of the radius 7 is formed at all vertices of quadrilateral .
To Find : sum of areas of all sectors
Solution:
Let say ABCD is quadrilateral
Area of circle = πr² where r is radius
Area of sector = ( sector angle° / 360°)πr²
Area of sector at vertices A = ( A° / 360°)π7²
Area of sector at vertices B = ( B° / 360°)π7²
Area of sector at vertices C = ( C° / 360°)π7²
Area of sector at vertices D = ( D° / 360°)π7²
Total area
= π7²(A° + B° + C° + D° ) / 360°
Sum of angles of a quadrilateral = 360°
=> A° + B° + C° + D° = 360°
Hence Total area = π7²(360° ) / 360°
= π7²
using π = 22/7
= (22/7)7²
= 22 x 7
= 154 sq units
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