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 ...
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Dropping perpendiculars splits the difference into two segments of (40 – 20) / 2 = 10 cm. Height is √(26² – 10²) = √(676 – 100) = √576 = 24 cm. Area is (1/2) x (40 + 20) x 24 ...
In rectangle ABCD, base AD = 8 cm and perpendicular height from vertex E to AD is 10 cm. The area of triangle ADE is (1/2) x base x height = (1/2) x 8 x 10 = 40 cm².
Perimeter of a circle is 2 x π x r, directly proportional to radius r. Therefore, the ratio of circumferences C1 / C2 = (2πr1) / (2πr2) = r1 / r2 = 5 / 4, so ratio of radii is ...
(i) Square side 14 cm gives 4 semicircles of diameter 14 cm; each petal side is a quarter circle of radius 7 cm, totaling 8 x (π x 7 / 2) = 88 cm. (ii) Hexagon side 42 cm gives ...