Midpoints cut each corner triangle’s area to 1/4 of its diagonal triangle. Summing opposite corner triangles removes 1/4 + 1/4 = 1/2 of the total 4-gon area, leaving exactly half for the inner Varignon parallelogram.
Discussion Forum Latest Questions
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.
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 ...
(i) One revolution covers circumference π x d = (22/7) x 56 = 176 cm (1.76 m). (ii) In 10 km (1,000,000 cm), number of revolutions is 1000000 / 176 = 5681.82, or approximately 5682 revolutions.
Using perimeter formula 2 x π x r = 44 with π = 22/7, we get 2 x (22/7) x r = 44. Dividing both sides by 44/7 gives radius r = 7 cm.