Perimeter of Complex Shapes
Complex shapes are made by combining or removing simpler shapes. To find the perimeter, identify all outer edges and sum their lengths, using geometry rules where sides are unknown.
What You Need to Know
Key Concept Diagram
Perimeter is the total distance around the outside of a shape
For composite shapes, identify which edges form the outer boundary
Missing side lengths can be found using the properties of rectangles and other shapes
Semicircle perimeters include the curved arc (pi x r) plus any straight edges on the boundary
Key Vocabulary
Perimeter
The total length of the outer boundary of a shape
Composite shape
A shape made by combining two or more simple shapes
Arc
A curved portion of a circle's circumference
Missing side
A length not given directly but calculable from other measurements
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
An L-shaped figure has outer dimensions 10 cm x 8 cm with a 4 cm x 3 cm rectangle removed from one corner. What is the perimeter?
Question 2
A shape consists of a rectangle 6 m x 4 m with a semicircle on one 6 m end. What is the perimeter? (use pi = 3.14)
Question 3
A running track consists of two straight sections of 80 m and two semicircles of diameter 40 m. What is the total distance around the track? (pi = 3.14)
Key Concepts Summary
- ●Perimeter is the total distance around the outside of a shape
- ●For composite shapes, identify which edges form the outer boundary
- ●Missing side lengths can be found using the properties of rectangles and other shapes
- ●Semicircle perimeters include the curved arc (pi x r) plus any straight edges on the boundary