Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Calculating the exact shaded area.
Notice;
Square side is 4 units.
Small regular hexagon side is 2 units.
Big regular hexagon side is 4 units.
Therefore;
Area shaded, exactly in square unit decimal is;
Area square with side 4 units - Half area small regular hexagon + Area triangle with height 2.53589838486 units and base 4√(3) units + Area triangle with height 4 units and base 4sin60 units.
= 4² - ½(6√(3)) + ½(2.53589838486*4√(3)) + ½(4*4sin60)
= 16 - 3√(3) + 8.78460969082 + 4√(3)
= 16 + √(3) + 8.78460969082
= 26.5166604984 square units exactly in decimal.
