Question

A square is inscribed in a circle of diameter 12 millimeters. What is the area of the shaded region? A square is inscribed in a circle with a diameter of 12 StartRoot 2 EndRoot millimeters. Everything outside of the square is shaded. Recall that in a 45 – 45 – 90 triangle, if the legs each measure x units, then the hypotenuse measures x units. (72π – 144) mm2 (72π – 72) mm2 (288π – 288) mm2 (288π – 144) mm2

Answer 1

Answer:  A. (72π - 144) mm²

Step-by-step explanation:

$A_{shaded}=A_{circle}-A_{square}\\\\\\A_{circle}=\pi \cdot r^2\\.\qquad \ =\pi \bigg(\dfrac{12\sqrt2}{2}\bigg)^2\\\\.\qquad \ =\pi (6\sqrt2)^2\\.\qquad \ =72\pi\\\\\\A_{square}=side^2\\.\qquad \quad =\dfrac{12\sqrt2}{\sqrt2}^2\\\\.\qquad \quad =12^2\\\\.\qquad \quad =144\\\\\\\large\boxed{A_{shaded}=72\pi-144}$