The base of the side of a regular triangular prism is 6cm and the diagonal of the side edge is 10cm

| March 17, 2021 | education

The base of the side of a regular triangular prism is 6cm and the diagonal of the side edge is 10cm. Find the lateral and total surface area of a prism?

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 = 36 * √3 / 4 = 9 * √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 = 100 – 36 = 64.

AA1 = 8 cm.

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

Side = Ravs * AA1 = 3 * AB * AA1 = 3 * 6 * 8 = 144 cm2.

Then Sпов = Sbok + 2 * Sсн = 144 + 2 * 9 * √3 = 18 * (8 + √3) cm2.

Answer: The lateral surface area is 144 cm2, the total surface area is 18 * (8 + √3) cm2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.