Hexagon

ABCDEF is a hexagon. G, H, I, J, K, and L are midpoints on AB, BC, CD, DE, EF, and FA respectively. M is a point inside ABCDEF. Connecting M to the 6 midpoints dissects the hexagon into 6 small quadrilaterals. The vertices of each small quadrilateral includes a shared vertex with ABCDEF, two midpoints adjacent to the shared vertex, and the interior point M. Starting from the quadrilateral with vertex A, going clockwise, the areas of the first five quadrilateral are 81, 64, 49, 36, and 25, respectively. What’s the area of the remaining quadrilateral (the one with vertex F)?

Pokémon cards

Leo collects Pokémon cards. Kyle, Issaic, and Dr. Hong look at his card box and then have the following conversation with Leo --

• Kyle: Leo has at most 65 cards;
• Issaic: Leo has at least 70 cards;
• Dr. Hong: Leo has at least 58 cards.

If exactly one of them is false, what’s the smallest number of cards Leo has?

Adding Square Roots

Calculate:

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