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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. See more

Level 2

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 the 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?

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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