Problem of the Week
Problem B
Share and Share Alike

Monique, Thibaut, Bastien, and Sylvie are siblings who share an irregularly-shaped room in their home. They have divided up the room so that each person has their own space. Each person’s space is either a rectangle, a trapezoid, or a triangle. A floor plan, including some dimensions, is shown in the following diagram.

A composite shape made up of four spaces labelled Monique, Thibaut, Bastien, and Sylvie. The perimeter of the composite shape is a solid line and dashed lines divide the interior of the shape.

Thibaut's space is a trapezoid with two vertical parallel sides of different lengths and horizontal bottom side of length 4 metres.

Monique's space is a rectangle with horizontal sides of length 6 metres and vertical sides of length 3 metres. The right vertical side of Monique's space is the left vertical side of Thibaut's space and is marked with a dashed line.

Bastien's shape is a rectangle with horizontal sides of length 4 metres and vertical sides of length 5 metres. The left vertical side of Bastien's space is the right vertical side of Thibaut's space and is marked with a dashed line.

The bottom sides of Monique, Thibaut, and Bastien's spaces lie along a horizontal line. Sylvie's space is a right-angled triangle with a horizontal side lying along this same horizontal line and a vertical side extending the right vertical side of Bastien's rectangle downward. The horizontal side of Sylvie's space is a dashed line with length 7 metres. The vertical side has length 4 metres.

Calculate the area of each person’s space. Which person has the space with the largest area?

The siblings have decided to divide up the room in a different way so that the area of each person’s space is equal. After they do this, what is the area of each person’s space?

Redraw the inner dashed lines in the floor plan so that the area of each person’s space is equal. Note that the shape of each person’s space may no longer be a rectangle, trapezoid, or triangle.