Respuesta :

Since you already have the radius (7.53), you must find the area of the circle and subtract the area of the square from that. So, you use the formula A = [tex] \pi [/tex] r^2 where r is 7.53. From there, you get about 178.1311 square cm. Then, knowing the diagonal (7.53 * 2 or 14.06), you get the side length to be about 10.65. Squaring that, we get 113.4225. Subtracting, we get the answer to be about 64.7 square centimeters.

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The area of a circle:

[tex]A_C=\pi r^2\\\\r=7.53\ cm\\\\A_C=\pi\cdot(7.53)^2=56.7009\pi\ cm^2\approx56.7009\cdot3.14\approx178.04\ cm^2[/tex]

The area of a square (like an area of a rhombus):

[tex]A_S=\dfrac{d\cdot d}{2}=\dfrac{d^2}{2}\\\\d=2\cdot7.53=15.06\ cm\\\\A_S=\dfrac{(15.06)^2}{2}=\dfrac{226.8036}{2}=113.4018\ cm^2\approx113.40\ cm^2[/tex]

The area of the yellow region:

[tex]A=A_O-A_S\\\\A=178.04-113.40=64.64\ cm^2\approx64.6\ cm^2[/tex]

Answer: 64.4 cm²

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