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A chocolate dessert in the shape of a square Pyramid. The Pyramid is represented with a net. How many square inches of icing are needed for the faces of the dessert
To find the total surface area of the square pyramid-shaped chocolate dessert, we need to find the area of each face and then add them all together.
Since a square pyramid has 4 equal triangular faces and a square base, the total surface area is calculated as follows:
1. The area of the square base:
Let's say the base of the square pyramid has a side length of s inches. The area of the square base is s^2 square inches.
2. The area of each triangular face:
Each triangular face of the pyramid is an isosceles triangle with a base equal to the side length of the square base and a height that forms one of the slant heights of the pyramid (let's call it h). The area of each triangular face is 0.5 * base * height.
Since the base is s inches and the height is h inches, the area of each triangular face is 0.5 * s * h square inches.
Since there are 4 triangular faces on a square pyramid, the total area of all 4 faces is 4 * 0.5 * s * h = 2 * s * h square inches.
Adding the area of the square base and the total area of the triangular faces, we get the total surface area of the square pyramid:
Total Surface Area = s^2 + 2 * s * h square inches.
Therefore, the total area of icing needed for the faces of the chocolate dessert in the shape of a square pyramid is (s^2 + 2 * s * h) square inches.