Understanding the Right Triangle
To find the area of a right triangle, we need two sides: the base and the height. In this case, we know the base is 16 cm, and the hypotenuse is 34 cm.
Applying the Pythagorean Theorem
We can use the Pythagorean theorem to find the height (the other side) of the triangle. The theorem states:
- (Hypotenuse)² = (Base)² + (Height)²
Plugging in the known values:
- 34² = 16² + Height²
- 1156 = 256 + Height²
- Height² = 1156 - 256
- Height² = 900
- Height = √900 = 30 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 = (Base x Height) / 2
Substituting the values we found:
- Area = (16 cm x 30 cm) / 2
- Area = 480 cm² / 2
- Area = 240 cm²
Final Result
The area of the right triangle with a base of 16 cm and a hypotenuse of 34 cm is:
- 240 cm²
This area calculation demonstrates how to apply the Pythagorean theorem in conjunction with the area formula for right triangles.