What is the surface area of a square pyramid with base length of 10 cm and slant height of 20 cm? (1 point )
The surface area of a square pyramid can be found by adding the area of the base to the area of the four triangular faces.
The area of the base of a square pyramid is calculated by squaring the length of one side of the square base. In this case, the base length is 10 cm, so the area of the base is (10 cm)^2 = 100 cm^2.
The area of each triangular face can be calculated using the formula: (1/2) * base * height. In this case, the base of each triangular face is the same as the base length of the square base, so it is also 10 cm. The height can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the slant height) is equal to the sum of the squares of the two legs (the height and half the base).
Thus, the height can be found as: (slant height)^2 - (1/2 * base)^2 = 20^2 - (1/2 * 10)^2 = 400 - 25 = 375. Taking the square root of 375 gives us the height of the triangular face, which is approximately 19.36 cm.
The total surface area of the square pyramid can therefore be calculated as 100 cm^2 (for the base) + 4 * ((1/2) * 10 cm * 19.36 cm) (for the four triangular faces). Simplifying this gives:
100 cm^2 + 4 * (5 cm * 19.36 cm) = 100 cm^2 + 76.8 cm^2 = 176.8 cm^2.
Therefore, the surface area of the given square pyramid is approximately 176.8 cm^2.