Way 1: Since 7² + 24² = 49 + 576 = 625 = 25², it is a right triangle, so Area = (1/2) x 7 x 24 = 84 cm². Way 2: Semi-perimeter s = 28 cm; Heron’s formula yields ...
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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.
Let square side be s. The sum of heights to AB and CD equals s, so Area(ΔPAB) + Area(ΔPCD) = (1/2) x s x s = s²/2. Both regions equal half the square’s area, making their ratio 1:1.
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 ...