The base of the pyramid is an isosceles triangle, the base of which is 16 cm, and the lateral side is 10 cm.

| March 26, 2021 | education

The base of the pyramid is an isosceles triangle, the base of which is 16 cm, and the lateral side is 10 cm. A cone is inscribed in the pyramid. Find the area of the axial section of the cone if its height is 9 cm.

Determine the radius of the inscribed circle in the isosceles triangle ABC.

The semi-perimeter of the triangle is: p = (AB + AC + BC) / 2 = (16 + 10 + 10) / 2 = 18 cm.

Then R = (AB / 2) * √ ((2 * AC – AB) / (2 * AC + AB)) = (16/2) * √ ((2 * 10 – 16) / (2 * 10 + 16 )) = 8 * √ (4/36) = 8 * (2/6) = 16/6 = 8/3 = 2 (1/3) cm.

Then the diameter of the inscribed circle is: D = MK = 2 * R = 16/3 = 5 (1/3) cm.

The axial section of the inscribed cone is the DMC triangle, in which the cone height is the triangle height, and the cone diameter is the base of the triangle.

Then Ssec = MK * DO / 2 = (16/3) * 9/2 = 24 cm2.

Answer: The area of the axial section of the cone is 24 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.