Mensuration
152. Triangle's Total Length · Adding up the three sides
The perimeter is always the sum of the three side lengths.
Perimeter of a triangle = a + b + c, the sum of its three side lengths. The same formula whether the triangle is equilateral, isosceles, or scalene.
What this lesson covers
Try to break it
Drag A, B, or C. Squash the triangle nearly flat or stretch it tall — the three side lengths change, but the perimeter is always AB + BC + CA. Try to get a perimeter that isn't the sum of the sides — impossible.
How you build it
Make a triangle.
- Place point A, the first vertex of the triangle.
- Place point B, the second vertex of the triangle.
- Place point C, the third vertex of the triangle.
- Draw segment AB of the triangle.
- Draw segment BC of the triangle.
- Draw segment CA to complete the triangle.
The proof, step by step
Prove that the perimeter of a triangle is the sum of its three sides.
- The perimeter of a polygon is the total length of its boundary.
- A triangle has three sides: a, b, and c.
- Adding these lengths gives the total boundary length: P = a + b + c.
Worked example
A triangle has side lengths of 7 cm, 24 cm, and 25 cm. What is its perimeter?
Perimeter = Sum of all sides = 7 + 24 + 25 = 56 cm.
- 56 cm — correct
- 66 cm
- 76 cm
- 86 cm