Question

Pls help me on 103 :((

Answer 1

Answer: H

Explanation:

Finding the Diameter

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.

`2*3=6`

Finding the Length of One Side

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.

`(6)/(√(3))`

The length of one side of the square is
`(6)/(√(3))`

Finding the Area

As we already know the length of one side, we can just square it to get the area.

`((6)/(√(3)))^2`

`(6^2)/((√(3))^2)` [Properties of Exponents]

`(36)/(3)`

`12`

Hence, the area of the square is 12 cm².

Answer 2

J)
`18cm^2`

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.