Answer :
Answer:
[tex]Area\ of\ th\e metal\ frame = 65.5x^{2}\ (unit)^{2}[/tex]
Step-by-step explanation:
Assuming that the metal frame is a square metal frame because the length of the side of the metal frame is given.
Given:
Radius of the mirror = 2x unit
Side length of the square metal frame = 12x unit
We need to find the area of the metal frame.
Solution:
First we find the area of the circular mirror, using area formula of the circle.
[tex]A_{c} = \pi r^{2}[/tex]
Where, r = Radius of the object.
Substitute r = 2x in above equation.
[tex]A_{c} = \pi (5x)^{2}[/tex]
[tex]A_{c} = \pi (25x^{2})[/tex]
[tex]A_{c} = 25\pi x^{2}\ (unit)^{2}[/tex]
Now, we find the area the square, using area formula of the square.
[tex]A_{S} = (Side\ length)^{2}[/tex]
[tex]A_{S} = (12x)^{2}[/tex]
[tex]A_{S} = 144x^{2}\ (unit)^2}[/tex]
So, the area of the square metal frame is given as
[tex]A_{f}=A_{s}-A_{c}[/tex]
[tex]A_{f}=144x^{2}-25\pi x^{2}[/tex]
[tex]A_{f}=(144-25\pi) x^{2}[/tex]
[tex]A_{f}=(144-25\times 3.14) x^{2}[/tex]
[tex]A_{f}=(144-78.5) x^{2}[/tex]
[tex]A_{f}=65.5 x^{2}\ (unit)^{2}[/tex]
Therefore, the area of the metal frame is [tex]65.5x^{2}\ (unit)^{2}[/tex].