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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.

Hazri aligned two identical ordinary pencils in such a way that the pencil tips are stuck together as shown in the 2D (flat) diagram above.

If the angles formed by the pencil tips in the 2D diagram are both \( 40 ^ \circ \), then what is the value of \(x\) in degrees?

What is the area of the large square?

Line segments are drawn from the vertices of the large square to the midpoints of the opposite sides to form a smaller white square.

If each red or blue line-segment measures \(10\) m long, what is the area of the smaller, white square in m\(^{2}?\)

Which route has a shorter distance?

**Route A**

**Route B**

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