A net of a square based pyramid is shown below 10m 15m what is the surface in square meters of the pyramid
To find the surface area of the pyramid, we need to find the areas of all the individual triangular faces and the square base.
The area of each triangular face can be found using the formula for the area of a triangle: Area = (1/2) * base * height.
In this case, the base of each triangular face is one side of the square base, which is 10m. The height of each triangular face is the slant height of the pyramid.
To find the slant height, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle, with the base of the triangle being one side of the square base (10m) and the height being the diagonal of the square base.
Since the diagonal of a square can be found using the formula diagonal = side * sqrt(2), the height of each triangular face is 10m * sqrt(2).
Therefore, the area of each triangular face is (1/2) * 10m * 10m * sqrt(2) = 50m^2 * sqrt(2).
Since there are 4 triangular faces, the total area of all the triangular faces is 4 * 50m^2 * sqrt(2) = 200m^2 * sqrt(2).
The area of the square base can be found by squaring one side of the square. In this case, the area of the square base is 10m * 10m = 100m^2.
Therefore, the total surface area of the pyramid is 200m^2 * sqrt(2) + 100m^2 = 100m^2 * (2 + sqrt(2)).
To find the numerical value, we can use a calculator or approximate the value of sqrt(2) to 1.41.
Therefore, the surface area of the pyramid is approximately 100m^2 * (2 + 1.41) = 341m^2.