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medium difficulty5 min

Coordinate-based perimeter

Perimeter is the total length around the boundary of a figure drawn using coordinates.

In one line: Perimeter means the full walk around the shape.

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Understand it

To find perimeter on a coordinate plane, calculate each side length with the distance formula and then add them all. The key idea is to walk around the outside edge, not across the figure. This concept often appears in triangle and quadrilateral questions.

Formula and rule

Perimeter = sum of all boundary side lengths.

Each side can be found by the distance formula if coordinates are given.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

For a triangle with side lengths 3, 4, and 5, perimeter = 3 + 4 + 5 = 12 units.

Method you can reuse

  1. 1Find each side length.
  2. 2Keep the sides in boundary order.
  3. 3Add every side.
  4. 4Simplify carefully.
  5. 5Write the answer with units.

Sketch it in your answer

Mark the vertices in order around the boundary so that no side is missed and no diagonal is counted.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A triangle has side lengths 3 units, 4 units, and 5 units. What is its perimeter?

Think first, then show answer
The perimeter is 12 units because perimeter means the sum of all three side lengths: 3 + 4 + 5 = 12.

Common wrong answer

A common wrong answer is 9 units because students add only two sides or leave out one boundary length.

Don't mix this up

Students sometimes add coordinates or only two sides instead of adding every side around the shape.

Exam tip

Write the side lengths one by one in order around the figure, then add them at the end.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Find the perimeter of a triangle or quadrilateral from coordinates, or compare the perimeter of two shapes on a graph.
  1. 1

    Enough for 1 mark

    Perimeter is the total length around the boundary of a figure drawn using coordinates.

  2. 2

    Add for 2 marks

    Example: If a triangle has side lengths 3, 4, and 5 units, its perimeter is 12 units.

  3. 3

    Add for 3 marks

    To find perimeter on a coordinate plane, calculate each side length with the distance formula and then add them all.

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