The figure below is supposed to show three non-overlapping shapes– one oval and two triangles. Which one of the following figures P, Q, R, or S fits the missing portion indicated by ‘?’ and completes the oval and the two triangles?

The correct option/figure is P.

To determine which figure completes the oval and the two triangles, we can analyze the missing portions of the three shapes in the main figure step-by-step:

1. Completing the Oval (Top-Left Shape):
The top-left shape in the main figure is an oval with its bottom-right quarter missing. The cutout has a vertical edge on the left and a horizontal edge at the top.
To complete the oval, the missing piece must be a quarter-oval sector with a vertical boundary on the left, a horizontal boundary on the top, and a curved edge on the bottom-right.
Comparing the options, figures P, Q, and R contain this correct quarter-oval piece, whereas figure S contains a much larger semi-oval piece, which is incorrect.

2. Completing the Bottom Triangle:
The bottom shape in the main figure is a trapezoid, which represents a triangle with its top vertex cut off. The top edge of this trapezoid is horizontal, and its sides slope downward and outward.
To complete it into a triangle, the missing piece must be a triangle pointing upwards with a horizontal base.
In figure P, the bottom piece is an upward-pointing triangle with a horizontal base, which perfectly continues the sloped sides of the trapezoid.
In figure Q, the bottom piece is a right-angled triangle, which is incorrect because it does not match the symmetric sloping sides of the trapezoid.

3. Completing the Top-Right Triangle:
The top-right shape in the main figure is a triangle with a square/rectangular cutout in its bottom-left region. This cutout is bounded by a horizontal edge on the top and a vertical edge on the right.
To complete this triangle, the missing piece must have a horizontal top edge, a vertical right edge, and a sloped bottom edge that aligns with the rest of the triangle's outline.
Comparing the remaining options:
- In figure P, the top-right piece has a horizontal top boundary, a vertical right boundary, and a sloped bottom-left boundary, fitting the cutout perfectly.
- In figure R, the top-right piece is a downward-pointing triangle that does not have the vertical right edge required to mate with the cutout.

By combining these findings, only figure P provides the correct matching pieces to complete the oval and the two triangles without overlap.