Question

AREA ADDITION AND SUBTRACTION URGENT?

Answer 1

Okay, so we know that the radius of the circle is 7.53

The area of the circle is 178.13, so we'll remember that.

Because the diameter is 15.06, we actually realize that the square is now two triangles, with the hypotenuse being 15.06.

a^2 + b^2 = 15.06^2

Now, because a^2 and b^2 are of the same value, we can basically turn it into this:

2a^2 = 226.8036

a^2 = 113.4018

Doing this actually solves for the square's area:

178.13 - 113.4018 = 64.7282

The yellow region is 64.7282 cm^2

Answer 2

The area of a circle:

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

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

$A_S=\dfrac{d\cdot d}{2}=\dfrac{d^2}{2}\\\\d=2\cdot7.53=15.06\ cm\\\\A_S=\dfrac{15.06)^2}{2}=\dfrac{226.8036}{2}=113.4018\ cm^2\approx113.40\ cm^2$

The area of the yellow region:

$A=A_O-A_S\\\\A=178.04-113.40=64.64\ cm^2\approx64.6\ cm^2$

Answer: 64.4 cm²