Mathematics Question and Solution
Calculating Area Red.
a² = 6²+8²
a = √(100)
a = 10 cm.
a is the side length of the square.
6b+8b+10b = 8*6
24b = 48
b = 2 cm.
b is the radius of the inscribed circle.
tanc = 6/8
c = atan(3/4)°
cosc = 2/d
d = 2/cos(atan(3/4))
d = 2.5 cm.
e = 90-c
e = atan(4/3)°
tane = f/2.5
(4/3) = f/2.5
f = 2.5(4/3)
f = ⅓(10) cm.
f = 3.333 cm.
g = (½(c)+90)°
g = (0.5atan(3/4)+90)°
h² = (8-2)²+2²
h² = 40
h = 2√(10) cm.
j² = 10²+(2√(10))²-2*10*2√(10)cos(0.5atan(3/4)+90)
j = 13.416407865 cm.
(13.416407865/sin(0.5atan(3/4)+90)) = (2√(10)/sink)
k = 26.5650511771°
tank = l/10
l = 5 cm.
It implies;
Area Shaded Red is;
10²-(½(2.5)(10/3))-(½*10*5)
= 100-(5/4)(10/3)-25
= 75-(25/6)
= ⅙(450-25)
= ⅙(425) cm²
= 70.83 cm²
