ABCA1B1C1 is a regular triangular pyramid, points K, O are the midpoints of A1B1 and A1C1, respectively.

| February 14, 2021 | education

ABCA1B1C1 is a regular triangular pyramid, points K, O are the midpoints of A1B1 and A1C1, respectively. Calculate the area of the triangle BC1K if BC = 6cm, AA1 = √15

Since the prism is correct, an equilateral triangle lies at its base, and the side faces are perpendicular to the bases.

The edge ABB1A1 is perpendicular to the base of A1B1C1, then C1K is perpendicular to ВK, and the triangle BC1K is rectangular.

From the right-angled triangle КВ1В, according to the Pythagorean theorem, we define the hypotenuse КВ.

KB ^ 2 = BB1 ^ 2 + KB1 ^ 2 = 3 ^ 2 + (√15) ^ 2 = 9 + 15 = 24.

CВ = √24 = cm.

In triangle A1B1C1, we determine the length of the median C1K.

Since A1B1C1 is an equilateral triangle, then C1K = B1C1 * √3 / 2 = 3 * √3 cm.

Determine the area of ​​the triangle BC1K.

Svs1k = C1K * ВK / 2 = 3 * √3 * √24 / 2 = 3 * 6 * √2 / 2 = 9 * √2 cm2.

Answer: The area of ​​the triangle is 9 * √2 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.