Question

Enola is buying a rug with a square and rectangle pattern. The rug is placed on a coordinate plane as shown here. Find the percentage of the rug that is in orange.

Answer 1

I don’t have the diagram you mentioned. Could you either upload the image or type the coordinates/dimensions of the square and rectangle pattern (or describe which parts are orange)?

If you want to try it yourself, here are the steps and two ways to compute the percentage:

Method A — simple rectangle/square areas
1. Find the total rug area (width × height for the outer rectangle or side² for an outer square).
2. Find the total orange area by summing areas of the orange rectangles/squares and subtracting any overlaps.
3. Percentage orange = (orange area / total area) × 100%.

Method B — polygon coordinates (useful if shapes are rotated or irregular)
1. List the vertices of each polygon (outer rug and each orange region) in order.
2. Use the shoelace formula to get each polygon’s area:
Area = 1/2 · |Σ (x_i y_{i+1} − x_{i+1} y_i)|, with x_{n+1}=x_1.
3. If there are multiple orange polygons, add their areas, subtract overlaps if any (compute overlap polygon area by intersection).
4. Percentage = (orange area / total area) × 100%.

If you post the picture or the coordinates/dimensions, I’ll compute the exact percentage for you.