Find the area of regular octagon with each side ‘a’ cm. -Maths 9th

Find the area of regular octagon with each side ‘a’ cm. -Maths 9th
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Answer :

(a) 2a2 (1 + √2) Let ABCDEFGH be the regular octagon of side a cm. Now if we produce the sides of the octagon on both the sides, we get a square PQRS. Given, BC = DE = FG = HA = a cm. Also, BQ = QC = DR = RE = FS = SG = HP = PA = \(rac{a}{\sqrt2}\)(∵ BQC, DRE, FSG, HPA are rt. ∠d Δs)∴ Side of square = \(rac{a}{\sqrt2}\) + a + \(rac{a}{\sqrt2}\) = a (1 + √2) cm.∴ Area of square = a2(1 + √2)2 cm2 = a2(3 + 2√2) cm2 Each of the shaded Δs, APH, BCQ, DER, FGS is an isosceles right angled Δ, whose area= \(rac{1}{2} imesrac{a}{\sqrt2}\) x \(rac{a}{\sqrt2}\) cm2 = \(rac{a^2}{4}\) cm2∴ Area of octagon = Area of square PQRS – Total area of shaded isosceles Δs = a2 (3 + 2√2) - a2= 2a2 (1 + √2) cm2.
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The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m2. -Maths 9th

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A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, -Maths 9th

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