Understanding the Right Triangle
A right triangle is defined by one 90-degree angle and has three sides: the hypotenuse (the longest side opposite the right angle) and the two legs (the sides that form the right angle). In this case, the hypotenuse is given as 10 cm, and one leg (the base) is 6 cm.
Finding the Other Leg
To find the area of the triangle, we first need to determine the length of the other leg (height). We can apply the Pythagorean theorem, which states:
- The square of the hypotenuse equals the sum of the squares of the other two sides.
Using this theorem:
- Hypotenuse^2 = Base^2 + Height^2
- 10^2 = 6^2 + Height^2
- 100 = 36 + Height^2
- Height^2 = 100 - 36
- Height^2 = 64
- Height = √64 = 8 cm
Calculating the Area
Now that we have both the base and height, we can calculate the area of the triangle using the formula:
- Area = (1/2) × Base × Height
Substituting the values:
- Area = (1/2) × 6 cm × 8 cm
- Area = 3 cm × 8 cm
- Area = 24 cm²
Final Result
The area of the right triangle with a hypotenuse of 10 cm and a base of 6 cm is:
- 24 cm²