The imaginary shape... :)
Really it is a hexagonal prism.
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Only equiangular and regular hexagons have six equal angles. Hexagons do not have to have six equal angles, and the only way a hexagon can have six equal angles if it is equiangular or regular.
Oh, that's a happy little question! In a 6x6 grid, you have 36 individual squares. But if you count all the different sizes of squares that can fit within the grid, including the whole grid itself, you have a total of 91 squares to enjoy painting with your imagination.
A net with six squares can make a cube, if drawn correctly.
Areas are measured in squares.The area of any shape is the number of squares that it covers. The number of squares covered depends upon the size of the squares.A square centimetre is a square with 1 centimetre along each side.If you had a square 6 centimetres along each side, how many of these "square centimetres" would be needed to fill its interior?First, along one edge of the square you could fit 6 of these square centimetres in a row.You could also fit 6 of these rows down the 6 cm square. So in total there would be 6 x 6 = 36 of the little squares:.............................................................----------------------..........|.....|......|.....|......|......|.....|..........|--+--+--+--+--+--|..........|.....|......|.....|......|......|.....|..... In this diagram, each little square is a square with.....|--+--+--+--+--+--|..... 1 cm along each side......|.....|......|.....|......|......|.....|..... The big square is 6 cm along each side, and you can.....|--+--+--+--+--+--|..... see the 36 little squares inside it in 6 rows of 6 little.....|.....|......|.....|......|......|.....|..... squares in each. To count the squares quickly, the.....|--+--+--+--+--+--|..... sides of the square are multiplied together......|.....|......|.....|......|......|.....|..........|--+--+--+--+--+--|..........|.....|......|.....|......|......|.....|..........----------------------.............................................................
Let the numbers be m & m+1 (consecutive) Hence their squares are m^2 & ( m + 1)^2 => m^2 & m^2 + 2m + 2 Hence Their sum is m^2 + m^2 + 2m + 1 = 85 2m^2 + 2m - 84 = 0 m^2 + m - 42 =0 Factor (m + 7)(m - 6) = 0 Hence the numbers are 6 & 7 .