Question

A deck has side lengths 16 feet, 18 feet, 16 feet, 8 feet, and 12 feet.
The dimensions of a proposed deck are written on the floor plan. What is the area of the proposed deck? Round to the nearest square foot.

317 square feet
413 square feet
437 square feet
513 square feet

Answer 1

I can’t determine the area from just the five side lengths — I need the floor‑plan figure or a description of how the sides are joined (the order of the sides and the angles between them). Could you either

- upload a picture of the floor plan, or
- describe the polygon in order (e.g. “sides of lengths 16, 18, 16, 8, 12 in that cyclic order, with right angles between the 16–18 and 18–16 sides, etc.”)?

If the figure is an orthogonal plan (only right angles), a quick way to solve it is:
1. Put one vertex at (0,0) and walk around the polygon using the given side lengths and the directions shown on the plan to get vertex coordinates.
2. Compute the area with the shoelace formula, or decompose the figure into rectangles/triangles and sum/subtract their areas.

If you post the image or the order/angles I’ll compute the area and pick the correct choice.