The area, in square centimeters, of the shaded quarter of the circle is π cm² OR 3.14 cm²
Calculating the area of a sector
From the question, we are to determine the area of the shaded quarter of the circle
The shaded quarter of the circle is a sector.
The area of a circle is given by the formula,
[tex]A = \frac{\theta}{360^\circ}\times \pi r^{2}[/tex]
Where A is the area
θ is the angle subtended
and r is the radius
First, we will calculate the radius of the circle
The radius of the circle equals the length of a side of the square.
From the given information,
Area of the square = 4 cm²
∴ s² = 4 cm²
s =√4 cm²
s = 2 cm
∴ A side of the square is 2 cm in length
Thus,
r = 2 cm
and
θ = 90°
Then,
[tex]A = \frac{90^\circ}{360^\circ}\times \pi \times 2^{2}[/tex]
[tex]A = \frac{1}{4}\times \pi \times4[/tex]
[tex]A = \pi \ cm^{2}[/tex] OR 3.14 cm²
Hence, the area, in square centimeters, of the shaded quarter of the circle is π cm² OR 3.14 cm²
Learn more on Calculating the area of a sector here: https://brainly.com/question/3539709
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