¶ 2022 AMC8 Problem 1
Problem:
The Math Team designed a logo shaped like a multiplication symbol, shown below on a grid of -inch squares. What is the area of the logo in square inches?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The multiplication symbol consists of squares, each measuring inch by inch, surrounded by right triangles, each exactly half of a square. Thus the total area of the logo is square inches.
By the Pythagorean Theorem, each 1-by-1-inch square has a diagonal length of . The multiplication symbol consistes of congruent squares of side length . Therefore the total area of the logo is square inches.
The logo can be enclosed in a large square of side length 4. There are 12 right triangles, each with area square inch, that are outside the logo and inside that square. The area of the logo equals the area of the large square minus the area of the triangles:
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions