Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Calculating the circle's radius, r.
The radius of the circle is;
Area triangle with base 21 cm and height r cm + Area triangle with base 15 cm and height r cm + Area triangle with base 12√(2) cm and height r cm = Area triangle with base 21 cm and height 12√(2)sin45 cm
½(21r) + ½(15)r + ½(12√(2)r) = ½*21*12√(2)sin45
21r + 15r + 12√(2)r = 21*12√(2)sin45
(36+12√(2))r = 252r
r = 252/(36+12√(2)) cm.
r = 3(3-√(2)) cm.
It implies;
The exact area of the Circle in terms of π square cm is;
πr²
= π(9-3√(2))²
= 9π(11-6√(2)) cm²
