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(49) In the diagram, ABCD is a unit square. Arc AC has center D and arc BD has center C.
Find the shaded area in square units.
Link to diagram: https://ibb.co/zhCbbmhz
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The shaded area is the sum of areas of two 60°-degrees sectors of a circle of the radius of 1 unit
minus the area of the equilateral triangle with the side length of 1.
The area of one 60°-sector of a circle of the radius 1 is 1/6 of the area of the circle, i.e.
= .
The area of the equilateral triangle with the side length 1 is .
Therefore, the shaded area is
+ - = - = - = - = 0.614184848 square units (approximately).
ANSWER. The shaded area is = 0.6142 square units (approximately).
Solved.