Question No:1
If the radius of each circle in the image is 6 cm, what is the area (in cm) of the quadrilateral formed by joining the centres of the
circles?
Answers
Given : radius of each circle in the image is 6 cm,
To Find : what is the area of the quadrilateral formed by joining the centers of the circles
36√3
64√3
72√3
84√3
Solution:
Quadrilateral ABCD is a rhombus with each side = 6 + 6 = 12 cm
one Diagonal AC = 6 + 6 = 12 cm
Quadrilateral ABCD can be split into two Equilateral triangles
ΔABC & ΔADC
Each of Side Equal to 12 cm
Area of Equilateral Triangle with side 12 cm = (√3/4)12²
= 36√3 cm²
Area of ΔABC = 36√3 cm²
Area of ΔADC = 36√3 cm²
Area of Quadrilateral ABCD = Area of ΔABC + Area of ΔADC
= 36√3 + 36√3
= 72√3 cm²
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