Final answer:
The total area of the four triangular faces of the right, square-based pyramid is 48 square units. This is found by calculating the area of one triangular face with the base of 6 units and height of 4 units and multiplying by four.
Step-by-step explanation:
The task is to calculate the total area of the four triangular faces of a right, square-based pyramid with base edges of 6 units and lateral edges of 5 units. To find the area of a triangular face, we need the base and the height of the triangle.
Since the base of the pyramid is a square, each triangular face will have a base of 6 units. The height of the triangular face can be found by creating a right triangle using the lateral edge (5 units) and half of the base (3 units) as legs. The height (h) is the other leg of the right triangle and can be found using the Pythagorean theorem: h = √(lateral edge2 - (base/2)2) = √(52 - 32) = √(25 - 9) = √16 = 4 units.
The area of each triangular face is given by the formula 1/2 × base × height, which is 1/2 × 6 × 4 = 12 square units. There are four identical triangular faces, so the total area is 4 × 12 = 48 square units.