In a straight triangular prism, the base of which is an equilateral triangle, the lateral edge is 2 dm

| September 7, 2021 | education

In a straight triangular prism, the base of which is an equilateral triangle, the lateral edge is 2 dm, and the lateral surface area is 24 dm. find the surface area of the prism.

In this case, it is useful to know that if an equilateral triangle lies at the base of a straight prism, then the prism is correct. This means that the areas of the three side faces are equal. Knowing the area of ​​the lateral surface, we find the area of ​​one face:
24: 3 = 8.
We have no limits to find the side of our equilateral triangle. This can be done quickly by knowing the side edge of the prism.
8: 2 = 4.
Find the area of ​​the lower base, which is an equilateral triangle.
S = 0.5 * 4 * 4 * sin 60 = 4 roots of 3.
S surface of the prism = 24 + 4 roots of 3 + 4 roots of 3 = 24 + 8 roots of 3 = 8 (3 + root of 3).
Answer: 8 (3 + root of 3).



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