Question 3
A rectangular sheet $20\,\mathrm{cm}$ by $30\,\mathrm{cm}$ is cut along dashed lines $AC,BD$ into four pieces: two congruent triangles and two congruent five-sided polygons, as in Figure I. Segments $AC,BD$ have equal lengths and meet at the rectangle's center at right angles.
a) What is the length of $AB$?
b) What is the area of a triangular piece? Of a five-sided piece?
c) Rearranging the four pieces forms a square with a rectangular hole, as in Figure II. What is the hole's area?
a) What is the length of $AB$?
b) What is the area of a triangular piece? Of a five-sided piece?
c) Rearranging the four pieces forms a square with a rectangular hole, as in Figure II. What is the hole's area?