Other leg is (2 x 54) / 12 = 9 cm. Hypotenuse is √(12² + 9²) = √(144 + 81) = √225 = 15 cm. Perimeter = 12 + 9 + 15 = 36 cm.
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A regular hexagon consists of 6 equilateral triangles of side r, giving area 6 x (√3/4)r² = (3√3/2)r². Dividing by circle area πr² gives (3√3) / (2π) ≈ 0.827, which is twice Question 8’s ratio because its area is double.
Radius is 10 cm. (i) Minor sector area is (90/360) x 3.14 x 10² = (1/4) x 314 = 78.5 cm². (ii) Major sector area is (270/360) x 3.14 x 10² = (3/4) x 314 = 235.5 cm².
Median AD divides ΔABC into equal areas: Area(ΔABD) = Area(ΔACD). Similarly, in ΔPBC, median PD gives Area(ΔPBD) = Area(ΔPCD). Subtracting these two equations yields Area(ΔABP) = Area(ΔACP).
Third side is 32 – (8 + 11) = 13 cm. Semi-perimeter s = 32 / 2 = 16 cm. By Heron’s formula, area = √(16 x (16 – 8) x (16 – 11) x (16 – 13)) = √(16 ...