find the surface area of a square pyramid with side length 4 cm and slant height 3 cm

Answer 1

The surface area of a square pyramid can be found by adding the area of the base with the area of the four triangular faces.

The base of the pyramid is a square, so the area of the base is calculated by squaring the length of one of its sides:
Area of base = (side length)² = 4² = 16 cm²

To find the area of each triangular face, we use the formula:
Area of triangle = 0.5 * (base length) * (height)

Since the slant height of the pyramid is given as 3 cm, the height of each triangular face can be found using the Pythagorean theorem. The height is the perpendicular side to the base, hence one of the right triangles formed by the slant height, the height, and half of the base length. The other two sides are the slant height (3 cm) and half of the base length (2 cm). Solving for the height (h) using the Pythagorean theorem:

h² + 2² = 3²
h² = 9 - 4
h² = 5
h = √5 ≈ 2.24 cm

Area of each triangular face = 0.5 * (base length) * (height) = 0.5 * 4 * 2.24 ≈ 4.48 cm²

Now, we can calculate the total surface area of the square pyramid:
Surface area = Area of base + 4 * Area of each triangular face
Surface area = 16 + 4 * 4.48 ≈ 16 + 17.92 = 33.92 cm²

Therefore, the surface area of the square pyramid is approximately 33.92 square centimeters.