Mathematics Question and Solution
Calculating area red.
a = 4+6 = 10 units.
a is the side length of the two congruent regular composite plane shape.
b = ½(10)
b = 5 units.
c = 5-1
c = 4 units.
tans = 4/6
d = atan(2/3)°
e² = 6²+4²
e = √(36+16)
e = √(52)
e = 2√(13) units.
f = 90-d
f = 90-atan(2/3)
f = atan(3/2)°
tanf = g/4
tan(atan(3/2)) = g/4
3/2 = g/4
g = 6 units.
It implies,
h = e
h = 2√(13) units.
i = 10-6-1
i = 3 units.
Therefore, area red is;
Area trapezoid with parallel sides 3 units and 5 units respectively, and height 10 units + Area triangle with height and base 2√(13) respectively.
= ½(3+5)*10 + ½(2√(13))²
= ½(80) + ½(52)
= 40+26
= 66 square units.
Or
Area square units side 10 units - 2(area triangle with height 6 units and base 4 units) - Area rectangle with length 10 units and width 1 unit.
= (10*10)-2(½*6*4)-(10*1)
= 100-24-10
= 100-34
= 66 square units.
