In a regular triangular pyramid, the side edge is 4 cm, and the side of the base is 6 cm. Find the side surface of the pyramid.
The side face of the pyramid is an equilateral triangle with side lengths of 4 cm and a base of 6 cm. Let’s draw the height DE of the triangle CDB. DE ^ 2 = CD ^ 2 – CE ^ 2 = 16 – 9 = 7.
СD = √7.
The area of the triangle CBD is S = 1/2 * CB * DE = 1/2 * 6 * √7 = 3 * √7.
Then the lateral surface area is S side = 3 * 3 * √7 = 9 * √7.
Answer: Side = 3 * 3 * √7 = 9 * √7.
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