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Answer:
J) [tex]18cm^2[/tex]
Step-by-step explanation:
a square inscribed in a circle means that the radius of the circle is the same thing as a line drawn from the center of the square to a corner.
this will give you the side measurements for a triangle (look at the attached picture). now use the Pythagorean theorem to find the hypotenuse aka the side length of the square. then multiply it by itself.
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Rewritten by : Barada
Answer: H
Step-by-step explanation:
If we draw a line through a diagonal of the square, two triangles are formed. The angle opposite the diagonal is 90°, as all angles are 90° in a square. One of the properties of a circle state that the angle in a semicircle is always 90°, which means that the diagonal formed a semi-circle.
A semi-circle only forms when a diameter is drawn in a circle, making the diagonal a diameter. This will be useful information, as we can calculate the side length of a square using the length of its diagonal.
A diameter is just twice the length of a radius, so the diagonal of the square would be 6 cm.
[tex]2*3=6[/tex]
The diagonal also splits the square into two 45-45-90 triangles. These triangles have a special property that their hypotenuse is √2 times each leg, and all legs are the same length.
Therefore, we can calculate the length of a leg by dividing the hypotenuse by √2.
[tex]\frac{6}{\sqrt{3}}[/tex]
The length of one side of the square is [tex]\frac{6}{\sqrt{3}}[/tex]
As we already know the length of one side, we can just square it to get the area.
[tex](\frac{6}{\sqrt{3}})^2[/tex]
[tex]\frac{6^2}{(\sqrt{3})^2}[/tex] [Properties of Exponents]
[tex]\frac{36}{3}[/tex]
[tex]12[/tex]
Hence, the area of the square is 12 cm².
