How to Calculate the Area A Using Pythagorean Theorem with 13mm and 12mm Sides

The Pythagorean theorem is a fundamental principle used in geometry to find the length of a side in a right triangle. It states:

a² + b² = c²

where c is the hypotenuse (the longest side), and a and b are the other two sides.

Given that you have two lengths: 13mm and 12mm, and want to find A, let's assume A is one of the sides in the right triangle.

Step 1: Identify the sides

• If 13mm is the hypotenuse (longest side), and 12mm is one leg, then:

Using the theorem:
A² + 12² = 13²

Now solve for A:

A² = 13² - 12² = 169 - 144 = 25

A = √25 = 5 mm

Step 2: Alternative (if 13mm and 12mm are legs and you want hypotenuse A)

If 13mm and 12mm are the legs, and A is the hypotenuse, then:

A² = 13² + 12² = 169 + 144 = 313

A = √313 ≈ 17.69 mm

Summary:

• If 13mm is the hypotenuse and 12mm is a leg, then A = 5 mm.
• If 13mm and 12mm are legs, then A (hypotenuse) ≈ 17.69 mm.

Make sure to know which side A refers to before applying the formula!