If a triangle has sides of lengths 3, 4, and 5, what is its area?

If a triangle has sides of lengths 3, 4, and 5, what is its area?

Step 1: Identify the lengths of the sides of the triangle. The sides are 3, 4, and 5.
Step 2: Check if the triangle is a right triangle. A triangle is a right triangle if the square of the longest side (5) equals the sum of the squares of the other two sides (3 and 4).
Step 3: Calculate the squares: 3^2 = 9, 4^2 = 16, and 5^2 = 25.
Step 4: Add the squares of the two shorter sides: 9 + 16 = 25.
Step 5: Since 25 (the sum of the squares of 3 and 4) equals 25 (the square of 5), the triangle is a right triangle.
Step 6: Use the formula for the area of a right triangle: Area = (1/2) * base * height.
Step 7: Choose the base as 3 and the height as 4.
Step 8: Substitute the values into the formula: Area = (1/2) * 3 * 4.
Step 9: Calculate the area: (1/2) * 3 * 4 = 6.

Area of a Triangle – The area of a triangle can be calculated using the formula (1/2) * base * height, especially applicable for right triangles.
Properties of Right Triangles – Recognizing that a triangle with sides 3, 4, and 5 is a right triangle allows for the use of the simpler area formula.