Number of triangle in octagon
Area of one triangle
Area of eight triangle = Area of Octagon
1080 sq in
The area of a regular polygon is half the product of its perimeter and the apothem, the height of a triangle whose base is one edge of the polygon. The octagon has 8 sides that are each 15 inches, so the perimeter is 8·15 in. Here, that means ...
... A = (1/2)Pa = (1/2)(8·15 in)·(18 in) = 1080 in²
The correct answer is b.
We know that the stop sign is in the shape of a regular octagon. Also, a regular octagon can be created using eight triangles of equal area.
We have the dimensions of one of this triangles. One triangle has a base of 20 inches and a height of 24 inches.
Wherever we have a triangle of base '''' and height '''' we can calculate its area using the following equation :
The area of one of this triangles using the equation (I) is :
To obtain the area of the stop sign we need to multiply the area of one single triangle by 8 (because a regular octagon can be created using eight triangles of equal area) ⇒
We found out that the correct answer is b.