+0  
 
0
363
1
avatar

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

Guest May 28, 2014

Best Answer 

 #1
avatar+26718 
+5

octagon

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°)

$${\mathtt{Area}} = {\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{9}}}^{{\mathtt{2}}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{22.5}}^\circ\right)}}} \Rightarrow {\mathtt{Area}} = {\mathtt{391.102\: \!597\: \!104\: \!531\: \!143\: \!5}}$$

Area ≈ 391.1 cm2

Alan  May 28, 2014
 #1
avatar+26718 
+5
Best Answer

octagon

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°)

$${\mathtt{Area}} = {\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{9}}}^{{\mathtt{2}}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{22.5}}^\circ\right)}}} \Rightarrow {\mathtt{Area}} = {\mathtt{391.102\: \!597\: \!104\: \!531\: \!143\: \!5}}$$

Area ≈ 391.1 cm2

Alan  May 28, 2014

16 Online Users

avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.