Given the three orthographic views of a solid as shown, find the volume of the solid.

Step 1: Analyze the orthographic views

The front view shows a trapezoid, indicating that the solid has varying depths or heights. The side view is a square with a diagonal, suggesting a prism-like structure or a wedge. The top view is an equilateral triangle with side length 2, which means the base of the solid is an equilateral triangle with side length 2.

Step 2: Determine the dimensions of the solid

From the top view, we know the base is an equilateral triangle with side length $a=2$. From the front view, the maximum height of the solid is $h=2$. The front view also shows that the solid can be decomposed into a triangular prism and a triangular pyramid.

Step 3: Calculate the area of the equilateral triangular base

The area of an equilateral triangle with side length $a$ is given by the formula $A = \frac{\sqrt{3}}{4} a^2$. Substituting $a=2$, we find the area of the base to be $\sqrt{3}$ square units.

Step 4: Decompose the solid into simpler shapes

Looking at the front view, the solid can be decomposed into two parts: a triangular prism with a height of 1 unit and a triangular pyramid with a height of 1 unit. Both share the same equilateral triangular base.

Step 5: Calculate the volume of the triangular prism

The volume of a prism is calculated by multiplying its base area by its height. Here, the base area is $\sqrt{3}$ and the height of this part of the solid is 1, so the volume of the prism part is $\sqrt{3}$ cubic units.

Step 6: Calculate the volume of the triangular pyramid

The volume of a pyramid is one-third of the product of its base area and its height. For the pyramid part of the solid, the base area is $\sqrt{3}$ and the height is 1, resulting in a volume of $\frac{\sqrt{3}}{3}$ cubic units.

Step 7: Calculate the total volume of the solid

The total volume of the solid is the sum of the volumes of the triangular prism and the triangular pyramid. Adding $\sqrt{3}$ and $\frac{\sqrt{3}}{3}$ gives a total volume of $\frac{4\sqrt{3}}{3}$ cubic units.

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