Mathematics Question and Solution
Calculating area blue.
tana = 24/32
a = atan(3/4)°
b² = 24²+32²
b = √(24²+32²)
b = 40 units.
c = b-20
c = 40-10
c = 30 units.
40 ~ 30
24 ~ d
Cross Multiply.
40d = 30*24
d = ¼(3*24)
d = 18 units.
d is the top parallel length of area blue.
f = 24-d
f = 24-18
f = 6 units.
g²+f² = 10²
g² = 10²-6²
g² = 100-36
g = √(64)
g = 8 units.
g is the height of area blue.
Therefore, blue area is;
½(24+d)*g
= ½(24+18)*8
= ½*42*8
= 21*8
= 168 square units.
