Grades 11-12 Video Solutions 2024-2024_11-12

Video Transcription

A triangular pyramid ABCD has sides of length 5, 6, 7, 8, 9, and 10. The points M, N, P, Q, R, and S are the midpoints of the edges of the pyramid as shown.  What is the perimeter of the closed hexagonal line M, N, P, Q, R, S, M?  We can use the triangle midpoint theorem first to find the line created by connecting the midpoints of two sides of a triangle is half the length of the third side.  Thus we know that MN is half of BC, MS is half of AC, and so on. Therefore we can find that the perimeter of our hexagon must be half of all of the sides  added together, which gives us the answer of 21.

Video Summary

A triangular pyramid ABCD has sides of length 5, 6, 7, 8, 9, and 10. The points M, N, P, Q, R, and S are the midpoints of the edges of the pyramid as shown. What is the perimeter of the closed hexagonal line M, N, P, Q, R, S, M? We can use the triangle midpoint theorem first to find the line created by connecting the midpoints of two sides of a triangle is half the length of the third side. Thus we know that MN is half of BC, MS is half of AC, and so on. Therefore we can find that the perimeter of our hexagon must be half of all of the sides added together, which gives us the answer of 21.