Given:
Radius of the circle = 4 meters
Measure of arc = 135 degrees
To find:
The area of the sector bounded by the given arc.
Solution:
Formula for area of a sector is:
[tex]A=\pi r^2\times \dfrac{\theta}{360^\circ}[/tex]
Where, r is the radius and [tex]\theta[/tex] is the central angle or measure of intercepted arc.
Putting [tex]r=4,\ \theta =135^\circ[/tex] in the above formula, we get
[tex]A=\pi \times (4)^2\times \dfrac{135^\circ}{360^\circ}[/tex]
[tex]A=\pi \times 16\times \dfrac{3}{8}[/tex]
[tex]A=\pi \times 2\times 3[/tex]
[tex]A=6\pi [/tex]
Therefore, the exact area of the given sector is [tex]6\pi [/tex] square meters.
