Mathematics Question and Solution
Notice.
The ascribed quadrilateral is a square.
Let it's side length be x.
a²+x² = 3²
a = √(9-x²) units.
2 ~ 3
b ~ x
Cross Multiply.
b = ⅓(2x) units.
It implies;
Calculating x.
x²-½(x*√(9-x²)) = ½(x+⅓(2x))*x
2x²-x√(9-x²) = ⅓(5x)*x
2x-√(9-x²) = ⅓(5x)
x = 3√(9-x²)
x² = 81-9x²
10x² = 81
x = ⅒(9√(10)) units.
x = 2.84604989415 units.
Again, x is the side length of the square.
cosc = 2.84604989415/3
c = 18.434948823°
sin18.434948823 = d/2
d = 0.63245553204 units.
e = x-d
e = 2.84604989415-0.63245553204
e = 2.21359436211 units.
The required area is;
½(2*3)+½(x*e)
= 3+0.5*2.84604989415*2.21359436211
= 3+3.15
= 6.15 square units.
