The base side of a regular triangular prism is 12cm, and the side diagonal is 13cm. Find the height of the prism

| August 18, 2021 | education

The base side of a regular triangular prism is 12cm, and the side diagonal is 13cm. Find the height of the prism, the perimeter of the base, the area of the lateral surface of the prism, the area of the base, the area of the total surface of the prism, the volume of the prism.

The perimeter of the base of the prism is: Ravs = 3 * AB = 3 * 12 = 36 cm.

Since the pyramid is regular, at its base lies an equilateral triangle ABC, the internal angles of which are 60, then Sbasn = AB ^ 2 * Sin60 / 2 = 144 * √3 / 4 = 36 * √3 cm2.

In a right-angled triangle ABA1, according to the Pythagorean theorem, we determine the length of the leg AA1.

AA1 ^ 2 = BA1 ^ 2 – AB ^ 2 = 169 – 144 = 25.

AA1 = 5 cm.

Let us determine the area of ​​the lateral surface of the prism.

Side = Ravs * AA1 = 3 * AB * AA1 = 3 * 12 * 5 = 180 cm2.

Then Sпов = Sbok + 2 * Sсн = 180 + 2 * 36 * √3 = 36 * (5 + 2 * √3) cm2.

Let’s define the volume of the prism.

V = Sbase * АА1 = 36 * √3 * 5 = 180 * √3 cm3.

Answer: Ravs = 36 cm, AA1 = 5 cm, Side = 180 cm2, Sb = 36 * √3 cm2, Spov = 36 * (5 + 2 * √3) cm2, V = 180 * √3 cm3.



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