Answer:
A = 240 units²
Step-by-step explanation:
the area (A) of a regular polygon is
A = [tex]\frac{1}{2}[/tex] pa ( p is the perimeter and a the apothem )
here p = 8 × 6 = 48 ( an octagon has 8 sides ) and a = 10 , then
A = [tex]\frac{1}{2}[/tex] × 48 × 10 = 24 × 10 = 240 units²
Answer:
Step-by-step explanation:
Preliminary task
Draw a regular octagon.
Draw a perpendicular from the side's midpoint to the center. (That is the apothem).
Draw two radii from the center of the side to the center of of the octagon. The endpoints of these two radii is the endpoints of the octagon's side.
The octagon has 8 such triangles.
Area one triangle
Area = 1/2 * side * apothem
side = 6
apothem = 10
Area = 1/2 6 * 10
Area = 30
Area of 8 such triangles.
Area = 8 * area of 1 triangle
area 1 triangle = 30
Area of 8 such triangles = 30*8 = 240
Answer 240
