Homework Help

concrete slab in the shape of a regular octagon. The distance from the centerup one of...

user profile pic

babylove12 | Student, Grade 10 | eNoter

Posted July 12, 2013 at 6:43 AM via web

dislike 1 like

concrete slab in the shape of a regular octagon. The distance from the centerup one of the peaks is 15 cm. Determine the area of a concrete slab

1 Answer | Add Yours

user profile pic

aruv | High School Teacher | Valedictorian

Posted July 12, 2013 at 7:04 AM (Answer #1)

dislike 1 like

Each interior angle of octagon= 135 degree.

`(angle s= ((n-2)xx180)/n)`

Draw a perpendicular from O to side of octagon ON .M is one vertex of octagone.

consider triangle OMN , OM=15 cm,

`angle M=(1/2)` of interior angle f octgon

=`135/2=62.5^o`

`angle n=90^o`

`ON=15xxsin(62.5^o)`

`MN= 15xx cos(62.5^o)`

`area of DeltaOMN=(1/2) xxMNxxON`

`=(1/2)(15^2)sin(62.5^o)cos(62.5^o)`

`` area of octagn=`16xx(1/2)xx(15^2) sin(62.5^o) cos(62.5^o)`

`=4xx15^2xxsin(135^o)`

`=636.40 ` sq cm.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes