Asked by Morgan Bradley on Jun 03, 2024
Verified
Gretchen is refinishing her gazebo that is in the shape of a regular octagon.The length of one side is 3 feet and the apothem is 3.5 feet.What is the area that Gretchen will be refinishing?
A) 10.5 sq feet
B) 24 sq feet
C) 42 sq feet
D) 63 sq feet
Apothem
A line segment that goes through the center of a polygon that is perpendicular to a side.
Octagon
A geometric figure with eight sides and eight angles.
Gazebo
A freestanding open structure, often found in gardens and parks, used for relaxation or entertainment.
- Apply mathematical skills to real-world scenarios about property management, including area calculations and cost estimations.
Verified Answer
MR
Manuel RibeiroJun 09, 2024
Final Answer :
C
Explanation :
The area of a regular polygon can be calculated using the formula 12×Perimeter×Apothem \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} 21×Perimeter×Apothem . For a regular octagon with each side of 3 feet and an apothem of 3.5 feet, the perimeter is 3×8=24 3 \times 8 = 24 3×8=24 feet. Thus, the area is 12×24×3.5=42 \frac{1}{2} \times 24 \times 3.5 = 42 21×24×3.5=42 square feet.
Learning Objectives
- Apply mathematical skills to real-world scenarios about property management, including area calculations and cost estimations.