The area of the metal frame is [tex]87.43x^2[/tex] sq. units.
Solution:
A circular mirror is surrounded by a square metal frame.
Radius of the circular mirror = 2x
Side length of the square frame = 10x
To find the area of the metal frame.
Area of the square frame = Side × Side
= [tex]10x \times 10x[/tex]
= [tex]100x^2[/tex] sq. units
Area of the square metal frame = [tex]4x^2[/tex] sq. units
Area of the circular mirror = [tex]\pi r^2[/tex]
= [tex]\frac{22}{7}\times(2x)^2[/tex]
= [tex]12.57 x^2[/tex] sq. units
Area of the circular mirror = [tex]12.57 x^2[/tex] sq. units
Area of the metal frame = Area of the square frame – Area of the mirror
= [tex]100x^2-12.57 x^2[/tex]
= [tex]87.43x^2[/tex] sq. units
Hence the area of the metal frame is [tex]87.43x^2[/tex] sq. units.
