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Write an expression in terms of pie that represents the area of the shaded part of N

Write An Expression In Terms Of Pie That Represents The Area Of The Shaded Part Of N class=

Sagot :

Let us write the formula for the area of the shaded portion,

[tex]\text{Area of a }\sec tor\text{=}\frac{\theta}{360}\times\pi r^2[/tex][tex]\begin{gathered} \text{where }\theta=360^0-75^0=285^0 \\ r=\text{radius}=x \end{gathered}[/tex]

Let us now solve for the area in terms of π,

[tex]\begin{gathered} \text{Area of the sector=}\frac{\text{285}^0}{360^0}\times\pi\times x^2 \\ =\frac{19}{24}x^2\pi \\ =0.7917x^2\pi\approx0.79x^2\pi\text{ (to nearest hundredth)} \end{gathered}[/tex]

Hence, the area in terms of π is 0.79x²π units.

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