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What is the area of a regular octagon, whose permineter is equal to 72 cm?

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What is the area of a regular octagon, whose permineter is equal to 72 cm?

Guest May 28, 2014

#1
+26550
+5

b = 72/8 cm = 9cm

tan(22.5°)=(b/2)/h  so h = (b/2)/tan(22.5°) cm

Area of 1/8 of Octagon = (b/2)*h = (b/2)2/tan(22.5°)

Area of Octagon = 8*(b/2)2/tan(22.5°)= 2b2/tan(22.5°)

$${\mathtt{Area}} = {\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{9}}}^{{\mathtt{2}}}}{\underset{\,\,\,\,^{{360^\circ}}}{{tan}}{\left({\mathtt{22.5}}^\circ\right)}}} \Rightarrow {\mathtt{Area}} = {\mathtt{391.102\: \!597\: \!104\: \!531\: \!143\: \!5}}$$

Area ≈ 391.1 cm2

Alan  May 28, 2014
Sort:

#1
+26550
+5

b = 72/8 cm = 9cm

tan(22.5°)=(b/2)/h  so h = (b/2)/tan(22.5°) cm

Area of 1/8 of Octagon = (b/2)*h = (b/2)2/tan(22.5°)

Area of Octagon = 8*(b/2)2/tan(22.5°)= 2b2/tan(22.5°)

$${\mathtt{Area}} = {\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{9}}}^{{\mathtt{2}}}}{\underset{\,\,\,\,^{{360^\circ}}}{{tan}}{\left({\mathtt{22.5}}^\circ\right)}}} \Rightarrow {\mathtt{Area}} = {\mathtt{391.102\: \!597\: \!104\: \!531\: \!143\: \!5}}$$

Area ≈ 391.1 cm2

Alan  May 28, 2014

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