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Geometry Warmups

Mathematics is filled with shapes that are kaleidoscopic in variety. Wielded since ancient times, the power of geometry helps us examine and measure these shapes.

Geometry Warmups: Level 1 Challenges

         

\[ 1^2 + 1^2 + 1^2 + 3^2 + 4^2 + 7^2 + 11^2 = \, ? \]

If lines \(l\) and \(m\) are parallel, then what is the value of angle \(x\) (in degrees)?

The diagram above shows a large square, whose midpoints are connected up to form a smaller square. We then connect up the midpoints of the smaller square, to obtain the inner shaded square.

What fraction of the large square is shaded?

Note: Give your answer as a decimal to 2 decimal places.

The picture above is a semicircle with diameter \(\overline{AC},\) and \(\overline{AC}\) is perpendicular to \(\overline{BD}.\) It is known that \(AB=4\text{ cm}\) and \(BC=1\text{ cm}.\) If \(BD=x,\) find \(x.\)

The clock shown has hands positioned at 5 o'clock. What is the degree measure of angle \(x\)?

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