Grades 11-12 Video Solutions 2021-video 2021 11-12/25

Video Transcription

Video Summary

The problem involves calculating the sum of numbers written on the faces of a rhombococcydodecahedron. This solid consists of 12 regular pentagonal faces, along with faces that are either equilateral triangles or squares. Each pentagonal face scores 5, each triangular face scores 1, and each square scores -1. The solid has 12 pentagons, 30 squares, and 20 triangles. Calculating the total score involves: 12 pentagons (12 x 5 = 60), 30 squares (30 x -1 = -30), and 20 triangles (20 x 1 = 20). Adding these gives 60 - 30 + 20 = 50. The answer is 50.

Keywords

rhombococcydodecahedron

geometric solid

face scoring

pentagon triangle square

total score calculation