How to Calculate the Area (A) Using the Pythagorean Theorem with Side Lengths 7cm and 4cm

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

a² + b² = c²

where c is the hypotenuse (the side opposite the right angle) and a and b are the other two sides.

If you have two sides of a right triangle measuring 7 cm and 4 cm, and you want to find the third side (which we'll call A), here are the steps:

1. Identify sides: Let's say 7 cm and 4 cm are the legs of the triangle (the shorter sides).
2. Apply the theorem:

Calculate the hypotenuse:

A = √(7² + 4²) = √(49 + 16) = √65 ≈ 8.06 cm

3. If instead, one of these (7 cm or 4 cm) is the hypotenuse and you want to find a leg, rearrange the formula:

For example, if 7 cm is the hypotenuse and 4 cm is a leg, find the other leg (A):

A = √(7² - 4²) = √(49 - 16) = √33 ≈ 5.74 cm

Ensure you know which sides you have (legs or hypotenuse) to use the formula properly. Also, note that the Pythagorean theorem applies only to right-angled triangles.