Treasure Island

Use the same map for two different tasks given:

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Task 2

 

Problem 95: Find the unshaded area

The circles in the rectangle are identical. Using coordinates, find the unshaded area inside the rectangle. Coordinates given belong to centre of the full circle.

Problem 94: Area Between 3-4-5 Triangles

Problem 93: Triangle or Square?

Problem 89: 90-60-30

【オリジナル問題】６
図のように、3つの角が30°・60°・90°の直角三角形を6個つなげたとき、AB：BC＝[ ]である。 pic.twitter.com/c7u2jBP0kT

— den@オリジナル問題集⊿ (@sansu_original) February 9, 2019

View image on Twitter AB/BC ?

Problem 79: Red Circle

Source: @TamasGorbe

Problem 77: Semicircles

Find the shaded area.

Source: Eylem Gercek Boss

Problem 74: Area

Problem 72: Square and Triangle

A square and an equilateral triangle together have the property that the area of each is the perimeter of the other.

Find the square's area.




Source: The Center of Math

Problem 68: Toppled Square

What is the area of the toppled square?

Resource: @Cshearer41

What’s the area of the toppled square? pic.twitter.com/77yHacED5Y

— Catriona Shearer (@Cshearer41) August 7, 2018

Problem 42: Pink Triangle

Although an easy one, @solvemymaths's following similarity question on Twitter went viral on the Internet, so I have decided to keep it here:

What fraction is shaded?

Platonic Solids

Plato and his disciples were so fascinated by the idea that there were only 5 regular polyhedra that each associated to a natural element: the tetrahedron with the fire, the Hexahedron to the Earth, the octahedron to the air, the dodecahedron to the cosmos and the icosahedron to water. (source)

Plato believed that geometry hid sacred truths describing reality. They say that when he founded the School of Athens in 387 BC he placed a sign at the entrance that said: "Let no one ignorant of the geometry between here."

Problem 36: Crescents=Triangle

I saw this lovely problem here.

Beautiful Gifs 4: Dynamic Müller-Lyer Illusions by Gianni A. Sarcone

Sarcone, Gianni A. "Dynamic Müller-Lyer Illusion." From Sarcone’s Studio -- A Sarcone & Waeber 

https://www.giannisarcone.com/Muller_lyer_illusion.html
Copyright © G. Sarcone