Calculate the perimeter of the given shape.

Question

ScanSolve AI Tutor · Accepted Answer

To find the perimeter of the shape, we need to sum the lengths of all its outer edges.

Identify all the outer edge lengths.
- The total width of the shape is the sum of the bottom horizontal segments: $15\text{m} + 6\text{m} + 15\text{m} = 36\text{m}$ . This is the length of the top horizontal edge.
- The left vertical edge is $24\text{m}$ .
- The bottom left horizontal edge is $15\text{m}$ .
- The inner left vertical edge is $8\text{m}$ .
- The inner horizontal edge (at the bottom of the cutout) is $6\text{m}$ .
- The inner right vertical edge is $8\text{m}$ .
- The bottom right horizontal edge is $15\text{m}$ .
- The right vertical edge is $24\text{m}$ .
Sum all the identified edge lengths to calculate the perimeter.
$\text{Perimeter} = 36\text{m} + 24\text{m} + 15\text{m} + 8\text{m} + 6\text{m} + 8\text{m} + 15\text{m} + 24\text{m}$ $\text{Perimeter} = (36 + 24 + 15 + 8 + 6 + 8 + 15 + 24)\text{m}$ $\text{Perimeter} = (60 + 15 + 8 + 6 + 8 + 15 + 24)\text{m}$ $\text{Perimeter} = (75 + 8 + 6 + 8 + 15 + 24)\text{m}$ $\text{Perimeter} = (83 + 6 + 8 + 15 + 24)\text{m}$ $\text{Perimeter} = (89 + 8 + 15 + 24)\text{m}$ $\text{Perimeter} = (97 + 15 + 24)\text{m}$ $\text{Perimeter} = (112 + 24)\text{m}$ $\text{Perimeter} = 136\text{m}$
The perimeter of the shape is $\text{136m}$ .

Answer