The area of the base of the regular quadrilateral pyramid is 36cm^2 and the area of a lateral face is 48cm^2. Find: Lateral area of the pyramid

To find the lateral area of the pyramid, we need to first determine the slant height of the pyramid. Once we have the slant height, we can calculate the lateral area using the formula: Lateral Area = (Perimeter of base) * (Slant height) / 2.

Let's break down the steps:

Step 1: Find the length of one side of the base of the pyramid.
Since it is given that the base of the pyramid is a regular quadrilateral (meaning it has four equal sides), we can find the length of one side by taking the square root of the area of the base. In this case, the area of the base is 36cm^2, so the length of one side of the base is √36 = 6cm.

Step 2: Find the perimeter of the base.
Since the base of the pyramid is a quadrilateral with four equal sides, the perimeter is simply 4 times the length of one side. In this case, the perimeter of the base is 4 * 6cm = 24cm.

Step 3: Find the slant height.
The slant height is the height of each triangular face of the pyramid. To find it, we can use the area of a lateral face. In this case, the area of a lateral face is given as 48cm^2. The formula for the area of a triangle is 1/2 * base * height. Since the base of the triangle is equal to the length of one side of the base of the pyramid (6cm), we can plug it into the formula: 48cm^2 = 1/2 * 6cm * height. Solving for height, we get height = (48cm^2) / (1/2 * 6cm) = 16cm.

Step 4: Calculate the lateral area.
Now that we have the perimeter of the base (24cm) and the slant height (16cm), we can calculate the lateral area using the formula: Lateral Area = (Perimeter of base) * (Slant height) / 2. Plugging in the values, Lateral Area = (24cm) * (16cm) / 2 = 384cm^2.

Therefore, the lateral area of the pyramid is 384cm^2.

It has 4 lateral sides

so the lateral area is 4 * 48

only the TOTAL area includes the base