Diagonal PR divides parallelogram PQRS into equal triangles PSR and PQR. Similarly, triangles OSR and OQR share base and equal heights, making their areas equal. Subtracting gives area(ΔPSO) = area(ΔPQO).
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Both triangles PCD and QCD share the common base CD and lie between parallel lines AB and CD, giving identical perpendicular heights. Hence their areas are equal, and the ratio area(ΔPCD) : area(ΔQCD) is 1:1.
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.
Arc length is (75/360) x 2 x (22/7) x 14 = (5/24) x 88 = 55/3 = 18.33 cm. Sector perimeter equals arc length plus two radii: 18.33 + 28 = 46.33 cm (or 46 and 1/3 cm).