Every year the students at Spotless Elementary do an outdoor cleanup.
First, the school yard is divided into three sections: \(A\), \(B\), and \(C\).
A map of the school yard is shown, with all given lengths in metres.
Note that the school yard is a square, the school is a rectangular
U-shape, and the diagram is not drawn to scale.
The school yard is a square
with two vertical sides (left and right) and two horizontal sizes (top
and bottom). The vertical and horizontal sides of the yard are each
\(70\) metres long.
The school is a rectangular U-shape with two vertical sides (left and
right) and four horizontal sides (one bottom, two top ends of the
U-shape, and one top side between the ends of the U-shape). The bottom
side is \(40\) metres long and the top
ends of the U-shape are each \(10\)
metres long.
The left side of the school is aligned with the left side of the
yard. The top ends of the U-shape of the school are \(10\) metres below the top side of the yard.
The top side of the school between the ends of the U-shape is \(30\) metres below the top side of the yard.
The bottom side of the school is \(20\)
metres above the bottom side of the yard.
Section A includes the region above the left top end of the U-Shape
and above the top side that is between the two ends of the U-shape.
Section B includes the region above the right top end of the U-Shape
and to the right of the right vertical side of the U-shape.
Section C is the remaining region of the yard.
The Grade \(1\) & \(2\) students are assigned the section with
the smallest area, the Grade \(5\)
& \(6\) students are assigned the
section with the largest area, and the Grade \(3\) & \(4\) students are assigned the remaining
section. Determine which section is assigned to each grade. Justify your
answer.
