How to Calculate Area and Perimeter of a Composite Figure

TL;DR

To calculate the area and perimeter of a composite figure like a novelty crown made from a rectangle with three semi-circles, first compute the perimeter by adding the lengths of the semi-circle arcs (3π each) to the rectangle's sides, giving you 58.27 inches. For the area, subtract the total area of the semi-circles from the rectangle's area, resulting in 65.5 square inches.

Transcript

a party goods company is making novelty crowns out of paper they start with a rectangular piece of paper and then cut three semi-circles each with a six inch diameter out of the top to create a crown so they start with a rectangle and then they cut these semi-circles out of the top of that rectangle find the area and perimeter of the crown below so... Read More

Key Insights

• 🙃 The perimeter of the crown is calculated by adding the lengths of the semi-circle arcs and the sides of the rectangle.
• ⚾ The area of the rectangle is obtained by multiplying its base and height.
• ⭕ The area of the semi-circles is found using the formula for the area of a circle and then dividing by 2.

Questions & Answers

Q: How do you calculate the perimeter of the paper crown?

To calculate the perimeter, add the lengths of the semi-circle arcs (3*pi) to the lengths of the sides of the rectangle (6+6+6+6), which gives a result of 58.27 inches.

Q: How is the area of the rectangle calculated?

The area of the rectangle is found by multiplying its base (18 inches) by its height (6 inches), giving an area of 108 square inches.

Q: What is the area of each semi-circle?

The area of a semi-circle with a radius of 3 inches is (9pi)/2 square inches. Since there are three semi-circles, the total area is 27pi/2 square inches.

Q: How is the area of the crown calculated?

The area of the crown is the area of the rectangle minus three times the area of the semi-circles. Substituting the values, it is 108 - (27*pi/2), which equals 65.59 square inches.

Summary & Key Takeaways

• A party goods company is making novelty crowns out of paper by cutting three semi-circles with a six-inch diameter out of the top of a rectangular piece of paper.

• In order to calculate the perimeter of the crown, the lengths of the semi-circles and the sides of the rectangle need to be added together.

• To find the area of the crown, subtract the area of the three semi-circles from the area of the rectangle.