The surface area of the square pyramid represented by the net is 96 cm²
Calculating the Surface Area of the Square Pyramid
To calculate the surface area of the square pyramid, we need to find the areas of the base and the four triangular faces.
Base Area:
The base of the pyramid is a square, so its area is given by:
Base area = (Side length)^2 = 4 cm * 4 cm = 16 cm²
Triangular Face Area:
The triangular faces of the pyramid are all congruent isosceles triangles. To find the area of one of these triangles, we can use the following formula:
Triangular face area = (Base length * Height) / 2
Using the given dimensions, we get:
Triangular face area = (4 cm * 6 cm) / 2 = 12 cm²
Total Surface Area:
The total surface area of the pyramid is the sum of the areas of the base and the four triangular faces. Therefore, we have:
Total surface area = Base area + 4 * Triangular face area
= 16 cm² + 4 * 12 cm²
= 96 cm²