CEMC Banner

Problem of the Week
Problem A
Quilting Puzzle

The employees of Sew Inspired need to make a tiny quilt for a special project using four different colours of fabric. Their quilt pattern is a rectangle divided into four smaller rectangles, marked \(A\), \(B\), \(C\), and \(D\).

A rectangle has a horizontal line dividing it into two smaller rectangles. In the top rectangle, a vertical line divides it further. The left side is marked A and the right side is marked B. In the bottom rectangle, a vertical line divides it further. The left side is marked C and the right side is marked D. The vertical separating A and B is to the left of the vertical line separating C and D.

Piece \(A\) is a square with area \(16~\text{cm}^2\) and piece \(D\) is a square with area \(25~\text{cm}^2\). The horizontal distance between the right side of piece \(A\) and the left side of piece \(D\) is \(2~\text{cm}\). What is the area of the entire quilt?

Themes: Geometry & Measurement, Number Sense