Understanding the Triangle
To find the area of a triangle when you have the base and the hypotenuse, you need to determine the height of the triangle. In this case, the base is 16 cm and the hypotenuse is 34 cm.
Step 1: Identify the Type of Triangle
- Since one side is the hypotenuse, we can assume this is a right-angled triangle.
- The hypotenuse (34 cm) is the longest side opposite the right angle.
Step 2: Apply the Pythagorean Theorem
- The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- Let the other side (height) be 'h'. We can express this as:
34^2 = 16^2 + h^2
- Calculate the squares:
1156 = 256 + h^2
- Rearranging gives:
h^2 = 1156 - 256
h^2 = 900
- Taking the square root, we find:
h = 30 cm
Step 3: Calculate the Area
- The area (A) of a triangle can be calculated using the formula:
A = (1/2) * base * height
- Plugging in the values:
A = (1/2) * 16 cm * 30 cm
- This simplifies to:
A = 240 cm²
Conclusion
- The area of the triangle is 240 cm².
- By identifying the height using the Pythagorean theorem, you can easily calculate the area of a right triangle with the given base and hypotenuse.