Answer:
60.7 cm² (nearest tenth)
Step-by-step explanation:
Square
From inspection of the diagram, we can determine that the side length of the square is 2 radii = 2 x 5cm = 10cm
Area of a square = side length x side length
⇒ area of square ABCD = 10 x 10 = 100 cm²
Square overlapping circle
All angles in a square measure 90°. Therefore, interior angle A and angle B of the square = 90°
Angles around a point add up to 360°. Therefore, the area of the square overlapping the circle = 360/90 = 1/4 of the area of the circle.
Area of a circle = [tex]\pi[/tex]r²
⇒ area of sector = 1/4 area of circle
= (1/4)[tex]\pi[/tex]r²
= (1/4)[tex]\pi[/tex]5²
= (1/4)[tex]\pi[/tex] x 25
= (25/4)[tex]\pi[/tex]
Shaded area
Shaded area = area of square - [2 x (1/4) area of circle]
= 100 - [2 x (25/4)[tex]\pi[/tex]]
= 100 - (25/2)[tex]\pi[/tex]
= 60.73009183...
= 60.7 cm² (nearest tenth)
