3D Pythagoras Flashcards

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c².

An extension of Pythagoras' Theorem used to find the length of a diagonal in a 3D shape.

The length of the diagonal is √(l² + w² + h²), where l, w, and h are the length, width, and height of the cuboid.

1. Identify the right-angled triangles. 2. Use Pythagoras' Theorem in two steps if needed. 3. Calculate the diagonal or required length.

Use Pythagoras' Theorem on one face: diagonal = √(l² + w²), where l and w are the dimensions of the face.

Use the formula √(l² + w² + h²) or apply Pythagoras' Theorem twice: first on a face, then with the height.

Always identify the right-angled triangle within the 3D shape before applying Pythagoras' Theorem.

Diagonal = √(3² + 4² + 5²) = √(9 + 16 + 25) = √50 = 7.07 (2 decimal places).

Find the slant height by identifying a right-angled triangle involving the height and half the base diagonal.

Forgetting to square all dimensions or missing a step when applying Pythagoras' Theorem twice.