Question

you are allowed to turn the small shapes.

Explanation:

Identify the given shapes

We are given two small shapes at the top:

1. An isosceles trapezoid.
2. A right triangle.

We need to determine which larger composite shape can be made by combining (composing) these two smaller shapes, allowing rotation.

Analyze the composite options

Let's look at the visible options:

• Top-left option: A shape resembling a mushroom or a tree, consisting of a semi-circular top and a trapezoidal trunk with inward cuts. This cannot be formed by joining a single trapezoid and a single right triangle.
• Top-right option: A shape with a curved top (semi-circle or circular arc) and a flat, tapered bottom. This also contains curved boundaries, which cannot be formed from a trapezoid and a triangle (both of which have only straight edges).
• Bottom-left option: A right triangle. This is just one of the starting shapes, not a combination of both.
• Bottom-right option: A larger triangle (looks like an isosceles triangle).

Let's evaluate if we can compose a larger triangle using the trapezoid and the right triangle:

• An isosceles trapezoid can be divided into a central rectangle and two congruent right triangles on either side.
• Alternatively, if we place a right triangle adjacent to one of the non-parallel sides of a trapezoid, we can complete a larger triangle. Specifically, if we take an isosceles trapezoid and attach a matching right triangle to one of its slanted sides, the slanted side of the trapezoid and the hypotenuse (or leg) of the triangle can align to form a single continuous straight boundary, resulting in a larger triangle.
• Therefore, the trapezoid and the right triangle can be put together to form the larger triangle shown in the bottom-right option.

Answer:

• (A) mushroom-like shape with curved top
• (B) cup-like shape with curved top
• (C) small right triangle
• (D) large triangle (Correct answer)