Mathematics Question and Solution
Calculating Red Area.
Let x be length AB equal length BD.
a²+3² = x²
a = √(x²-9) units.
It implies;
Calculating x
½(4+x)*3 = (3*x)+½(3√(x²-9))
12+3x = 6x+3√(x²-9)
12-3x = 3√(x²-9)
(4-x)² = x²-9
16-8x+x² = x²-9
25 = 8x
x = ⅛(25) cm.
x = 3.125 cm.
Again, x is length AB equal length BD.
cosb = 3/(3.125)
b = 16.2602047083°
c = 90+b
c = 106.2602047083°
Therefore, the required red area, area triangle ABD is;
½(x²)sinc
= 0.5*3.125²sin106.2602047083
= 4.6875 cm²
Or
Red Area is;
Area trapezoid with parallel lengths 4 cm and 3.125 cm respectively and height 3 cm - Area triangle with height and base 3 cm and 4 cm respectively.
= ½(4+3.125)*3-½(3*4)
= ½(3*7.125)-½(12)
= ½(21.375-12)
= ½(9.375)
= 4.6875 cm²
= 75/16 cm²
