The answer depends on the information provided. There is no simple formula unless the object is a regular tetrahedron. It may be necessary to make repeated use of Pythagoras's theorem on the base lengths and vertical height to calculate the slant heights, and use these to derive the area of each face. Not an easy task!
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you calculate the area of one side, then multiply it by three.
The question cannot be answered because, unfortunately, you forgot to say what book you are referring to.
The answer to this question depends on what sort of pyramid it is, and that depends on the shape of the base. You can get triangular pyramids (with a triangular base), square pyramids (like those in Egypt), pentagonal pyramids and so on. Let me take just one -- the square pyramid. Let the length of the base sides be 'a' units. Let 'h' units be the perpendicular height (i.e. at right angles to the base and going through the peak of the pyramid) of each side. I gather by lateral area that you mean surface area including the base. I use the symbol * to mean x or multiply. Then the formula for working out the surface area is a*a for the base PLUS each triangular face is 1/2*a*h There are 4 triangular sides so the surface area is (a*a) + 4*(1/2*a*h) If you just want the 4 sides, leave out a*a.
To calculate the surface area of a triangular prism, you need to find the area of the two triangular bases and the three rectangular faces. The formula for the surface area of a triangular prism is SA = 2B + PH, where B is the area of the base, P is the perimeter of the base, and H is the height of the prism. Given the bases are 4 cm^2 each and the sides are 10 cm^2, you would first find the perimeter of the base (P = 2s + b) and then calculate the surface area using the formula provided.
The surface area of prisms or pyramids are simply the total area of the corresponding nets.