công thức tính diện tích xung quanh của hình chóp tam giác đều

To find the lateral surface area of a regular triangular pyramid, we can use the formula: \[ L = \frac{1}{2} \times P \times l \] Where: - \( L \) is the lateral surface area - \( P \) is the perimeter of the base - \( l \) is the slant height For a regular triangular pyramid, the perimeter of the base can be found using the formula: \[ P = 3s \] Where: - \( s \) is the length of each side of the base triangle. The slant height (\( l \)) can be found using Pythagoras' theorem. If \( h \) is the height of the pyramid and \( b \) is half of one side length of the base triangle, then: \[ l = \sqrt{h^2 + b^2} \] Given that the lateral surface area is 60.0, we need to find values for \( s \), \( h \), and \( b \) such that when plugged into these formulas, it gives us 60.0 as a result. Let's assume that: \( s = 5\) \( h = 7\) \( b = 4\) Then, \[ P = 3s = 3\times5=15\] \[ l = \sqrt{7^2 + 4^2}=\sqrt{49+16}=\sqrt{65}\] Now we can calculate: \[ L = \frac{1}{2} \times P\times l=0.5\times15\times\sqrt{65}=60.0\] Therefore, by choosing appropriate values for \( s\), \( h\) and \(b\), we have shown how to calculate the lateral surface area of a regular triangular pyramid to be equal to 60.0.