Mathematics Question and Solution
Let r be the radius of the ascribed semi circle.
It implies;
r² = 14²+a²
a² = r²-196
a = √(r²-196) cm.
a is OA.
b = a+r
b = (√(r²-196)+r) cm.
b is AB.
Therefore, calculating r.
½*14*(√(r²-196)+r) = 147
7(√(r²-196)+r) = 147
(√(r²-196)+r) = 21
√(r²-196) = 21-r
r²-196 = (21-r)²
r²-196 = 441-42r+r²
42r = 441+196
42r = 637
6r = 91
r = 15⅙ cm.
r = 15.167 cm.
AB = √(r²-196)+r
AB = √((91/6)²-196)+(91/6)
AB = (35/6)+(91/6)
AB = 126/6
AB = 21 cm.
Therefore, green area is;
Area semi circle with radius (91/6) cm - 147 cm²
= ½(91/6)²π-147
= (8281π/72)-147
= (8281π-10584)/72 cm²
= 214.3267883941 cm²
= 214.33 cm² to 2 decimal places.
