Track / Stage 4 / 169 of 340 #429 of 1964

Problem 429

AMC 12 late, AIME early

Geometry Difficulty 4.8 Find the answer

A paper rectangle $3 \times 7$ was cut into squares $1 \times 1$ . Each square, except those that stood at the corners of the rectangle, was cut along both diagonals. How many small triangles were obtained?

Your answer

A number or a short expression. Spacing, $ signs and \frac vs / are all fine.

Official solution

Answer: 68.

Solution. Note that the total number of squares cut along the diagonals is $3 \cdot 7-4=17$ . Each of them is cut into 4 small triangles. Therefore, there will be $4 \cdot 17$ - 68 small triangles.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.