Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side length of the square be x.
Calculating x.
18²=x²+(x-6)²
324=x²+x²-12x+36
2x²-12x-288=0
x²-6x-144=0
(x-3)²=144+9
x = 3±√(153)
x ≠ 3-3√(17)
x = 3+3√(17) cm.
Therefore;
Area R to 1 d. p. in square cm is;
Area trapezoid with two parallel length 6 cm and (3+3√(17)) cm, and height (3+3√(17)) cm - 2(area triangle with height 10.6846584374 cm and width 6 cm) - Area sector with radius 12 cm and angle 58.633022225.
= ½(6+3+3√(17))*(3+3√(17)) - 2*½(6*10.6846584374) - (58.633022225÷360*144π)
= 164.215901262 - 64.1079506244 - 73.6804287519
= 26.427521886 cm²
≈ 26.4 cm²
