A stop sign is in the shape of a regular octagon. A regular octagon can be created using eight triangles of equal area. One triangle that makes up the stop sign has a base of 15 inches and a height of 18 inches. Calculate the area of the stop sign.

a. 1000 sq. in

b. 1080 sq. in

c. 980 sq. in

d. 1200 sq. in

1080 sq in

Step-by-step explanation:

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