Calculating the Semi-Perimeter

The semi-perimeter of a triangle is defined as half the sum of the lengths of its sides. In order to find the semi-perimeter of a triangle with side lengths of 20 cm, 15 cm, and 9 cm, we can follow these steps:

1. Calculate the sum of the lengths of all three sides:

20 cm + 15 cm + 9 cm = 44 cm

2. Divide the sum by 2 to find the semi-perimeter:

Semi-perimeter = 44 cm / 2 = 22 cm

Thus, the semi-perimeter of the triangle is 22 cm.

Explanation

In a triangle, the semi-perimeter is an important quantity that is often used in various mathematical calculations. It is denoted by the letter 's' and is calculated by adding up the lengths of all three sides and dividing the sum by 2.

The semi-perimeter is useful in many geometric formulas, such as Heron's formula for finding the area of a triangle. It is also used to calculate the radius of the triangle's inscribed circle and to determine the lengths of the triangle's altitudes.

In this particular case, we were given the lengths of the three sides of the triangle as 20 cm, 15 cm, and 9 cm. By adding up these lengths and dividing the sum by 2, we found that the semi-perimeter is equal to 22 cm.

Key Points
- The semi-perimeter of a triangle is half the sum of the lengths of its sides.
- It is denoted by the letter 's'.
- The semi-perimeter is useful in various geometric calculations.
- It is often used in formulas for finding the area, radius of the inscribed circle, and lengths of altitudes of a triangle.
- In this case, the semi-perimeter of the triangle with side lengths 20 cm, 15 cm, and 9 cm is 22 cm.