Surface Area Of Prisms & Pyramids

Explanation
The surface area of a rectangular prism can be found by adding up the areas of all six faces. In this case, the prism has two identical rectangular faces with dimensions 14 inches by 4 inches, two identical rectangular faces with dimensions 14 inches by 6 inches, and two identical rectangular faces with dimensions 4 inches by 6 inches. To find the surface area, we can calculate the area of each face and then add them all together. The area of each face is found by multiplying the length and width of the face. Therefore, the surface area of the prism is (14x4) + (14x4) + (14x6) + (14x6) + (4x6) + (4x6) = 280 + 280 + 84 + 84 + 24 + 24 = 776 square inches.

Explanation
The surface area of a cube is found by multiplying the length of one side by itself, and then multiplying that result by 6 (since a cube has 6 equal sides). In this case, the side length of the cube is given as 6.5 cm. Therefore, the surface area of the cube would be 6.5 cm * 6.5 cm * 6 = 253.5 cm².

Explanation
The provided image shows a triangular pyramid made up of congruent equilateral triangles. To find the surface area of the pyramid, we need to calculate the area of each triangular face and then add them together. Since the triangles are equilateral, we can use the formula for the area of an equilateral triangle, which is (sqrt(3)/4) * side^2. The image shows that each side of the triangle has a length of 4 units. Plugging this value into the formula, we get (sqrt(3)/4) * 4^2 = 4 * sqrt(3) units^2. Since there are 4 triangular faces, the total surface area of the pyramid is 4 * 4 * sqrt(3) = 16 * sqrt(3) units^2.