Page 123 - NUMINO Challenge_D1

14 Sam Loyd Puzzle

Basic Concepts Figure Puzzles

When you cut a rectangle into two stair shapes such that the widths and
lengths of both stair shapes are the same, you can make a new
rectangular or square shape.

You can also cut out various shapes and rearrange them into a rectangle
to help you find the area of the original figure.

Example The area of the obtuse triangle below can be found by changing
its shape into a rectangle that has the same base, and half the
height of the triangle. Try to make the rectangle with the least
number of pieces.

Class Notes

As shown on the right, cut the triangle along a line that passes
through the midpoint of the height, and is parallel to the base.
Then, cut the bottom piece along the line that is perpendicular
to the base, and passes through the vertex of the obtuse angle.
From the three pieces formed, rearrange the two triangles to make a rectangle that has
the same base, and half the height of the triangle.

Therefore, (Area of the Triangle) (Base) (Height)

120 NUMINO Challenge D1