Mathematics Question and Solution
a²+8² = 10²
a = 6 units.
a is AC,the height of triangle ABC.
Calculating b, radius of the inscribed circle.
10b+8b+6b = 8*6
24b = 48
b = 2 units.
c = 6-b
c = 4 units.
d = 8-b
d = 6 units.
e = 10-d
e = 4 units.
tanf = 8/6
f = atan(4/3)°
Therefore, area red is;
Area triangle with height 6 units and base 8 units - Area triangle with height 4 units and base 4sin(atan(4/3)) units.
½(6*8)-½(4*4sin(atan(4/3)))
= 24-8(4/5)
= ⅕(120-32)
= ⅕(88) square units.
= 17.6 square units.
