The area of the base is 28. The plane parallel to the plane of the base of the cone divides its height into

The area of the base is 28. The plane parallel to the plane of the base of the cone divides its height into segments by 4 and 4. Find the cross-sectional area of the cone by this plane.

The axial section of the cone will be an isosceles triangle, the lower base of which coincides with the diameter of the base of the cone.
The condition says that the area parallel to the base of the cone divides its height into equal segments of 4.
The same plane divides the height of the triangle in the axial section into the same parts. So the segment that divides the section is the middle line.
From this it follows that the diameter of the base is twice as large as the diameter of the obtained section.
Find the radius of the base of the cone. We find the area of ​​the circle by the formula S = πr² .:
28 = π * r²;
r² = 28 / π.
r = √ (28 / π).
Let us find the cross-sectional area of ​​the cone by the plane:
S = π * √ (28 / π) / 2 = π * √ (7 * 4 / π) / 2 = π * 2√ (7 / π) / 2 = π * √ (7 / π).
ANSWER: the cross-sectional area is π * √ (7 / π).