Shaded/green area will be;
Area semi circle of radius 9unit - 2(area sector of radius 9unit and angle 60°) + area equilateral triangle of single side length 9unit - area sector of radius 9unit a...
Notice;
Single interior angle of a regular polygon with 6 sides (regular hexagon) is 120°.
The formula to get it is;
(180°(n-2))/n.
Where n is the side number of the regular polygon....
Let the radius of the bigger circle be 2 unit.
Therefore the radius of the smaller circle will be;
½(2)=1 unit.
Let the radius of the semi circle be r.
It implies;
2² + r² = (1 + r)²...
Blue area will be;
Area square of single side length 4cm - 5(area circle of radius 1cm) + area square of single side 2cm.
= 16 - 5π + 4
= 20 - 5π
= 5(4 - π) cm²
Let x be a side length of the largest possible inscribed square of the scalene triangle with sides 13 cm, 14 cm and 15 cm respectively.
It implies;
x = 14÷((1/tan(53.13))+1+(1/tan(67.38)))...
Calculating x (radius of the small inscribed circle)
28² + x² = (56-x)²
784 + x² = 3136 - 112x + x²
112x = 2351
x = 21 units.
Calculating r, radius of the four congruent circles.
Area square with side 2r cm - Area circle with radius r cm = Area green.
(2r)² - πr² = 144π
4r² - πr² = 144π
(4-π)r² = 144π
r² =...
Area Area Blue is;
Area semi circle with radius √(2) units - Area quarter circle with radius 2 units + Area triangle with height and base 2 units respectively.
= ½(√(2)²)π - ¼(2²)π + ½(2²)...
Area Blue is;
Area triangle with height 4 cm and base (4sin150) cm
= ½*4*(4sin150)
= 2(4sin150)
= 8sin150
= ½(8)
= 4 cm²
Shaded Area is;
Area circle with diameter 30 cm - 7(area circle with diameter 10 cm)
= π(½(30))² - 7π(½(10))²
= π(15)² - 7π(5)²
= 225π - 175π
= 50π cm²
