Understanding and Applying the Pythagorean Theorem

The video introduces the Pythagorean theorem, explaining the formula C² = A² + B², where C is the hypotenuse of a right triangle and A and B are the other two sides.

An example is given with a right triangle where sides A and B are 5 and 12. The hypotenuse C is calculated to be 13 using the theorem.

The video shows how to solve for a side of a triangle when the hypotenuse is known, demonstrating simplification of radicals in the process.

A problem is presented involving a square with a diagonal length of 12 inches, using the theorem to find the side's length and calculate the area.

The video solves for the perimeter of a rhombus using its diagonals, applying the theorem to find the length of its sides.

The area of an isosceles trapezoid is calculated by finding the height using the Pythagorean theorem and then applying the area formula for trapezoids.