Mathematics Question and Solution
Notice;
a² = 5² - (⅕(√(481)))²
a = ⅕(12) units.
b = 5-a
b = ⅕(13) units.
c² = 4²-(⅕(12))²
c = ⅕(16) units.
d = atan(4/3)°
(a) Area A exactly is;
½*⅕(16)*(5+⅕(13)) - atan(4/3)π*16/360
= ((8*38)/25) - (2atan(4/3)π/45)
= (304/25) - ((2atan(4/3)π)/45)
= (2736-10πatan(4/3))/225 square units.
= 4.74163825599 square units.
(b) Calculating Area B to 2 decimal places.
½*10(10+5) - ½*⅕(16)(5+⅕(13)) - ((atan½+ata¾)π*16/360) - (⅕(13)*⅕(34-√(481))) - ½*⅕(√(481))(5+⅕(13)) - ((atan(12/√(481))+(2tan2-90))π*25/360) - (0.5*25sin(180-2tan2))
= 75 - 12.16 - 8.85718974235 - 6.27550965628 - 16.66810127159 - 14.30194776497 - 10
= 6.73725156481
≈ 6.74 square units.
