what is the surface area of a square pyramid where the base edge is 1.5 cm and the slant height is 4 cm

Answer 1

To find the surface area of a square pyramid, we need to add up the areas of all its faces.

First, let's find the area of the base by using the formula for the area of a square, where one edge is given:

Area of the base = (base edge)^2
Area of the base = (1.5 cm)^2
Area of the base = 2.25 cm^2

Now, let's find the areas of the four triangular faces.

To do this, we can use the formula for the area of a triangle, where the base and the height are known.

Area of a triangle = (1/2) * base * height

Since the height (slant height) of the triangular faces is given as 4 cm, we can use this for all four faces.

Area of each triangular face = (1/2) * base * height
Area of each triangular face = (1/2) * 1.5 cm * 4 cm
Area of each triangular face = 3 cm^2

Since there are four triangular faces, the total surface area of the square pyramid is:

Surface area = Area of the base + 4 * Area of each triangular face
Surface area = 2.25 cm^2 + 4 * 3 cm^2
Surface area = 2.25 cm^2 + 12 cm^2
Surface area = 14.25 cm^2

Therefore, the surface area of the given square pyramid is 14.25 cm^2.