A A trapezoid is divided into seven strips of equal width as shown. What fraction of the trapezoid's area is shaded? Explain why your answer is correct.
Solution. We can fit the trapezoid together with a rotated copy of itself to make a parallelogram:
The stripes on the two trapezoids join to make seven stripes across the parallelogram. These stripes are congruent to each other, so the shaded ones cover exactly $\frac{4}{7}$ of the area of the parallelogram. Since the two copies of the original trapezoid are identical, the stripes must also cover $\frac{4}{7}$ of the area of each trapezoid.