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Geometry

Geometry Warmups: Level 2 Challenges

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

A vertical 32-meter bamboo stick was broken by the wind, such that the tip meets the ground at a point 16 meters from the base. At what height above the ground (in meters) was it broken?

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