Answer: The area of the shape is 48.38 square centimeters.
Step-to-step explanation:-
The side-length of square = 15 cm
Area of square =[tex](\text{side}^2)=15^2=225\ cm^2[/tex]
Since, the figure shown is formed by the arcs joining the midpoints of the four sides of a square, the radius of the quadrant =[tex]\frac{15}{2}=7.5\ cm[/tex]
Since, all the interior angles in a square is a right angle, therefore, each quadrant is a sector of 90° in a circle of 7.5 cm radius.
Area of each quadrant= [tex]\frac{90^{\circ}}{360^{\circ}}\pi r^2[/tex]
=[tex]=\frac{1}{4}(3.14)(7.5)^2=44.15625\ cm^2[/tex]
Now, Area of shaded region = Area of square -4 × Area of quadrant
=[tex]225-4\times44.15625=48.375\approx48.38\ cm^2[/tex]
Hence, The area of the shape is 48.38 square centimeters.
