What is a polygon?
Figures can be open or closed, which may be made up of straight lines and curved lines, or made up of only curves, or only lines. If a figure is closed and made up of only line segments, it is called a polygon.
What is a triangle?
A triangle is a closed polygon made up of three line segments. So, a triangle has three sides, three vertices, and three angles. In geometry, a triangle is denoted by “△”. If there is a triangle whose vertices are A, B, and C, we can denote the triangle as △ABC.
What is the perimeter?
The perimeter of any figure is the total length of its boundary. And the perimeter of a polygon is calculated by adding all the sides of the polygon together. Since the perimeter is actually the length of the boundary of a closed shape, the unit of the perimeter is the same as that of the units of length, such as centimeter(cm), millimeter(mm), inch(in), feet(ft), yard(yd), kilometer(km), and mile(mi).
The perimeter of a triangle
The perimeter of a triangle is defined as the total length of the boundary. Since the boundary of the triangle is made by three line segments which are its sides, the perimeter of the triangle is equal to the sum of all three sides. If there is a triangle whose side lengths are a, b, and c, the perimeter of the triangle is equal to, a + b + c.
The perimeter of a △ABC = sum of all three sides
Hence, perimeter P = a + b + c
Rapid Recall
The perimeter of different types of triangles:
Solved Examples
Example 1: Find the perimeter of an equilateral triangle whose side length is 7 inches.
Solution:
The perimeter of an equilateral triangle, P = 3a
P = 3 \(\times\) 7
P = 21
So, the perimeter of the equilateral triangle is 21 inches.
Example 2: Find the perimeter of an isosceles triangle whose equal side lengths are 5 feet and the unequal side length is 7 feet.
Solution:
The perimeter of an isosceles triangle, P = 2a + b
P = 2 \(\times\) 5 + 7
P = 10 + 7
P = 17
So, the perimeter of the isosceles triangle is 17 feet.
Example 3: Find the perimeter of a triangle whose sides are 3 cm, 4 cm, and 5cm.
Solution:
The perimeter of a triangle P = a + b + c
P = 3 + 4 + 5
P = 12
So, the perimeter of the triangle is 12 centimeters.
A triangle has three vertices.
There are two equal sides in an isosceles triangle.
A triangle is made up of three line segments, so the sum of all three sides of a triangle gives us its perimeter.
An equilateral triangle has each angle equal to 60°.
P = 2a + b, where P is the perimeter of the isosceles triangle, a is the length of the equal sides, and b is the length of the third side.