Question

.



The polygon can be decomposed into two triangles to determine the area of the polygon. Which decomposition represents the area of the polygon?

A.
the area of triangle EFG plus the area of triangle CDE
B.
the area of rectangle ABCG plus the area of triangle CDE
C.
the area of triangle ABD plus the area of triangle AEF
D.
the area of rectangle ABDF plus triangle DEF
Part B
Multiple Choice Question
What is the area, in square units, of the polygon?
A.
12
B.
18
C.
24
D.
36

Answer 1

I don't have the diagram or the vertex coordinates, so I can't pick which decomposition is correct or compute the numeric area yet. Could you either

- upload the picture of the polygon, or
- describe the polygon (labels and coordinates or side lengths and right angles), or
- give the lengths of the segments shown (for example AB = ?, BC = ?, etc.)?

Meanwhile, here is how you can decide which decomposition is correct and how to compute the area once you have the necessary measurements:

1. Decide which decomposition is correct
- Sketch the polygon and draw the proposed diagonals for each choice.
- A valid decomposition must:
- Cover the entire polygon (no missing parts).
- Have pieces that lie entirely inside the polygon (no triangle part outside).
- Not double-count area (pieces should meet only along edges).
- Check each option by drawing it on the figure:
- If the proposed triangles/rectangle exactly partition the polygon, that option is correct.
- If a diagonal falls outside the polygon or leaves a gap, that option is wrong.

2. Compute areas
- Rectangle area = base × height.
- Triangle area = (1/2) × base × height (or use coordinates and the shoelace formula if you have vertex coordinates).
- Sum the areas of the pieces in the correct decomposition to get the polygon area.

If you send the diagram or the polygon’s dimensions, I’ll identify the correct decomposition and compute the area for Part B.