Question

Из какого наименьшего числа квадратиков 1*1 можно составить шестиугольник со сторонами 3, 7, 8, 10, 13 и 21?Варианты:147116126171

Answer 1

Правильний ответ 116 126

Answer 2

Forming a hexagon with the given side lengths

To form a hexagon with the specified side lengths of 3, 7, 8, 10, 13 and 21, we need to calculate the minimum number of 1x1 square tiles required.

The area of the hexagon can be calculated as:

Area = (1/2) × perimeter × apothem

Using the formula for the perimeter of a regular hexagon:

Perimeter = 6 × side length

And applying the given side lengths:

Perimeter = 6 × (3 + 7 + 8 + 10 + 13 + 21) = 6 × 60 = 360

The apothem can be calculated from the side length of 21 as:

Apothem = (√3/2) × 21 = 15√3

Therefore, the area is:

Area = (1/2) × 360 × 15√3 = 540√3

Since each 1x1 square tile has an area of 1, the minimum number of tiles needed is the ceiling of the calculated area, which is 147.

So the minimum number of 1x1 square tiles required to form this hexagon is 147.