Grades 9-10 Video Solutions 2026-2026_9-10

Video Transcription

Video Summary

Question 9. The diagram shows an equilateral triangle and three arcs, each centered at a different vertex of the triangle and with radius equal to the side length of the triangle. The side length of the equilateral triangle is 2 cm. What is the perimeter of the shaded shape? As we can see, the perimeter of the shaded shape is made up of three arcs. If we look at the angle from the arc, we know that it is an angle at a vertex of the triangle, which must be 60 degrees. And so our perimeter is made up of three 60 degree arcs. And we know that the circle must have radius 2, since the radius of the circle from which we are getting the arc is a side length of the equilateral triangle. Now we can evaluate what this is. So we have three, since there are three arcs, and then each arc, because it's a 60 degree arc, which is 1 6th of 360, the entire circle, is 1 6th of the circumference. And the circumference is 2 pi r, with r equals 2. So 2 times 2 pi times 1 6th times 3, which evaluates to 2 pi, or c.

Keywords

equilateral triangle

arcs

perimeter

radius

circumference