The edge or outline that separates the interior of a region from its exterior; the set of points on the dividing border.
A fence around a yardβit marks exactly where 'inside the yard' ends and 'outside' begins.
Showing a random 20 of 50 problems.
Example 1
medium
A 10 m by 6 m rectangle has a 2 m square cut out of one corner. Find the boundary length of the resulting L-shape.
Example 2
medium
A 12 m by 8 m yard has a square 3-by-3 m flowerbed inside it. What is the total boundary length, including the flowerbed?
Example 3
easy
What is the length of the boundary of a square with side 6 cm?
Example 4
easy
Which has a longer boundary: a circle of radius 5 or a circle of radius 2?
Example 5
medium
Two rectangles share one common 4 m edge. Rectangle A is 4 by 6 m, rectangle B is 4 by 5 m. What is the perimeter of the combined region?
Example 6
medium
A closed curve divides the plane into how many regions (besides the curve itself)?
Example 7
medium
A square garden has side 8 m. A path of width 1 m runs along the inside boundary. What is the inner edge's length?
Example 8
medium
The region R is defined by the inequalities xβ₯0, yβ₯0, and x+yβ€6. Describe the boundary of R and find its perimeter.Boundary of the region R: triangle with vertices (0,0), (6,0), (0,6); perimeter = 12 + 6β2
Example 9
medium
A 5 cm by 8 cm rectangle has fencing along its boundary at \$3 per cm. What is the cost?
Example 10
challenge
A rope of length 40 m is shaped into a closed curve enclosing maximum area. What is the shape and the area (use Οβ3.14)?
Example 11
challenge
Explain why the boundary of a region is itself a closed curve (has no boundary of its own), for a simple 2D region.
Example 12
medium
Why is the boundary of a region one dimension lower than the region itself?
Example 13
hard
A T-shape has top bar 8 wide, 2 tall and a vertical stem 3 wide, 6 tall centered below. Find its boundary length.
Example 14
hard
Among all rectangles with area 36, which has the smallest boundary length?
Example 15
easy
True or false: a point is part of the boundary if it is strictly inside the shape.
Example 16
challenge
Why can two regions have the same area but very different boundary lengths?
Example 17
medium
Does a region always have to be enclosed by a single boundary curve?
Example 18
medium
What is the dimension of the boundary of a 3D solid?
Example 19
medium
A right triangle has legs 6 and 8. Find its boundary length.
Example 20
challenge
An L-shaped region is made by removing a 2Γ2 square corner from a 6Γ6 square. Find the perimeter (boundary length).