Find the surface area for each of the following Rt. Square Pyramid
6.5cm 2.5cm,2.5cm
To find the surface area of a right square pyramid, you will need to calculate the area of each face and then add them together. A right square pyramid has a square base and four identical triangular faces.
1. Start by finding the area of the base. Since the base is square, you can use the formula for the area of a square: A = side^2. In this case, the side length is given as 2.5 cm, so the area of the base is 2.5 cm * 2.5 cm = 6.25 cm^2.
2. Next, calculate the area of a triangular face. Each triangular face is an isosceles right triangle, which means that two of its sides are equal in length. The two equal sides are the slant height of the pyramid, which is given as 6.5 cm. The formula for the area of an isosceles right triangle is A = (1/2) * leg^2, where leg represents the equal sides. In this case, the area of a triangular face is (1/2) * (6.5 cm)^2 = 21.125 cm^2.
3. Since there are four identical triangular faces, multiply the area of a single triangle by 4: 4 * 21.125 cm^2 = 84.5 cm^2.
4. Finally, add the area of the base and the total area of the triangular faces to find the total surface area of the pyramid: 84.5 cm^2 + 6.25 cm^2 = 90.75 cm^2.
Therefore, the surface area of the right square pyramid is 90.75 cm^2.