Question

A square stained glass window is divided into four congruent triangular sections by iron edging to represent the seasons of the year. Each diagonal of the square window measures 9 inches.

A square with diagonals is shown. The diagonals split the square into 4 congruent triangles. The uppercase left triangle is Fall, the uppercase right triangle is winter, the bottom left triangle is summer, and the bottom right triangle is spring.

What is the approximate total length of iron edging needed to create the square frame and the two diagonals?

43.5 inches
50.9 inches
54.0 inches
61.5 inches

Answer 1

Diagonal d = 9 in. For a square d = s√2, so side s = 9/√2 ≈ 6.364 in.

Frame perimeter = 4s ≈ 4(6.364) ≈ 25.456 in. Add two diagonals: 25.456 + 2(9) = 25.456 + 18 ≈ 43.456 in ≈ 43.5 in.

Answer: 43.5 inches.