The side of the base of a regular triangular prism is 2 cm, the side edge is 5 cm. find the volume of the prism and the area of the lateral surface.
1) At the base of a regular triangular prism lies an equilateral triangle with side a = 2 cm ..
V = Sb. * h; h is the height of the prism, it is equal to the length of the rib 5 cm.
Sosn. – the area of an equilateral triangle is calculated by the formula S = (√3) / 4 * a ^ 2;
Sosn. = (√3) / 4 * 2 ^ 2 = (√3) / 4 * 4 = √3 (cm ^ 2)
V = √3 * 5 = 5√3 (cm ^ 3)
2) The area of the lateral surface of a regular prism is equal to three areas of the lateral edge.
Sb.p. = 3Sgr .; Sgr. = ah;
Sgr. = 2 * 5 = 10 (cm ^ 2)
Sb.p. = 3 * 10 = 30 (cm ^ 2).
Answer. 5√3 cm ^ 3; 30 cm ^ 2.
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