Area of triangle using coordinates
This concept finds the area of a triangle directly from the coordinates of its vertices.
In one line: Triangle area from coordinates still follows half of base times height.
Practice This ConceptUnderstand it
When base and height are not easy to see, the coordinate area formula gives a reliable answer. It uses the coordinates in a fixed order and produces area without drawing measurements by hand. The absolute value is important because area must always be non-negative.
Example
Formula and rule
Area = 1/2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
For the points (1, 1), (5, 1), and (1, 4), area = 1/2 |1(1 - 4) + 5(4 - 1) + 1(1 - 1)| = 1/2 |-3 + 15 + 0| = 6 square units.
Method you can reuse
- 1Write the three vertices.
- 2Substitute them into the area formula.
- 3Simplify the bracket carefully.
- 4Take the absolute value if needed.
- 5Divide by 2 and write square units.
Sketch it in your answer
Plot the three points in order, join them, and watch for a right triangle or easy base-height pair when the graph makes it obvious.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
What is the area of the triangle with vertices (1, 1), (5, 1), and (1, 4)?
Think first, then show answerHide answer
Common wrong answer
A common wrong answer is 12 square units because students use base times height and forget the half.
Don't mix this up
Exam tip
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
- 1
Enough for 1 mark
This concept finds the area of a triangle directly from the coordinates of its vertices.
- 2
Add for 2 marks
Example: For vertices (1, 1), (5, 1), and (1, 4), the base is 4 units and the height is 3 units, so the area is 6 square units.
- 3
Add for 3 marks
When base and height are not easy to see, the coordinate area formula gives a reliable answer.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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