Mathematics Question and Solution
Calculating r, radius of the inscribed circle and area ABCD (isosceles trapezoid).
Notice.
Triangle AOD is a right-angled triangle
tana = 3/2
a = atan(3/2)°
tanb = 2/3
b = atan(2/3)°
Calculating r, radius of the inscribed circle.
sina = r/2
sin(atan(3/2)) = r/2
r = 1.66410058868 units.
Or
sinb = r/3
sin(atan(2/3) = r/3
r = 1.66410058868 units.
Calculating Area isosceles trapezoid ABCD.
c²+r² = 2²
c² = 2²-1.66410058868²
c = √(1.23076923075)
c = 1.10940039244 units.
d = 2c
d = 2(1.10940039244)
d = 2.21880078488 units.
d is AB.
e = 2r
e = 2(1.66410058868)
e = 3.32820117736 units.
e is the height of area ABCD.
f²+r² = 3²
f² = 3²-1.66410058868²
f = √(6.23076923075)
f = 2.49615088301 units.
g = 2f
g = 2(2.49615088301)
g = 4.99230176602 units.
g is CD.
Therefore, area ABCD is;
½(d+g)*e
= 0.5(2.21880078488+4.99230176602)*3.32820117736
= 12 square units.
