Mathematics Question and Solution
Let AD be 4 units.
Therefore;
AB will be;
½(AD)+½(½(AD))
AB = ½(4)+½(½(4))
AB = 2+1
AB = 3 units.
Area ABCD is;
4*3
= 12 square units.
Calculating Area Red (Area Trapezoid).
1 unit is the radius of the big inscribed quarter circle.
It implies;
a² = 2(1)²
a = √(2) units.
a is the height of the red area.
2 units is the radius of the bigger inscribed quarter circle.
It implies;
b² = 2²+2²
b = √(8)
b = 2√(2) units.
b is the top parallel length of the red area.
3 units is the radius of the biggest inscribed quarter circle.
It implies;
c² = 3²+3²
c = √(18)
c = 3√(2) units.
c is the bottom parallel length of the red area.
Therefore, area red is;
Area trapezoid with parallel lengths 2√(2) units and 3√(2) units respectively and height √(2) units.
= ½(2√(2)+3√(2))*√(2)
= ½*5√(2)*√(2)
= 5 square units.
Area Red/Area ABCD is;
5/12
