Assume that the large triangle in Stage 0 has a side length of 1 unit. What is the length of each side of the shaded triangle in 1? Explain. What is the perimeter of the shaded triangle in Stage 1? Explain. Find the sum of the perimeters of all the shaded triangles that are added at each stage. Fill in the table below. Perimeter of Total Perimeter Number of New Length of Each Stage Number Each New of New Triangles Side Triangle Triangles ½ 1 1 3/2 3/2 ¼ ¾ 2 3 9/4 3 4 5 Predict the perimeter of the new triangles that are added in stage 10.
Assume that the large triangle in Stage 0 has a side length of 1 unit. What is the length of each side of the shaded triangle in 1? Explain. What is the perimeter of the shaded triangle in Stage 1? Explain. Find the sum of the perimeters of all the shaded triangles that are added at each stage. Fill in the table below. Stage Number Number of New Triangles Length of Each Side Perimeter of Each New Triangle Total Perimeter of New Triangles 1 1 ½ 3/2 3/2 2 3 ¼ ¾ 9/4 3 4 5 Predict the perimeter of the new triangles that are added in stage 10.
alg_u1_i5_a152_sierpinskis_triangle.docx