The proportion of the Union Jack is 1:2 and was adopted 1801:
blue = RGBColor["#00247D"];
red = RGBColor[
"#CF142B"]; Graphics[{EdgeForm[{Black, Thickness[Large]}], {blue,
Polygon[{{0, (3 Sqrt[5])/2}, {0, 10}, {2 (10 - (3 Sqrt[5])/2),
10}}], Polygon[{{3 Sqrt[5], 0}, {25, 0}, {25,
1/2 (25 - 3 Sqrt[5])}}],
Polygon[{{35, 0}, {60 - 3 Sqrt[5], 0}, {35,
1/2 (25 - 3 Sqrt[5])}}],
Polygon[{{60, (3 Sqrt[5])/2}, {60,
10}, {60 - 2 (10 - (3 Sqrt[5])/2), 10}}],
Polygon[{{0, 20}, {0, 30 - (3 Sqrt[5])/2}, {2 (10 - (3 Sqrt[5])/2),
20}}], Polygon[{{3 Sqrt[5], 30}, {25, 30}, {25,
30 + 1/2 (-25 + 3 Sqrt[5])}}],
Polygon[{{35, 30}, {60 - 3 Sqrt[5], 30}, {35,
30 + 1/2 (-25 + 3 Sqrt[5])}}],
Polygon[{{60, 20}, {60,
30 - (3 Sqrt[5])/2}, {60 - 2 (10 - (3 Sqrt[5])/2), 20}}]}, {red,
Polygon[{{0, 0}, {3 Sqrt[5] + 2 (10 - (3 Sqrt[5])/2),
10}, {5 Sqrt[5] + 2 (10 - (3 Sqrt[5])/2), 10}, {2 Sqrt[5], 0}}],
Polygon[{{60, 0}, {60, Sqrt[5]}, {60 - 2 (10 - Sqrt[5]),
10}, {60 - 2 Sqrt[5] - 2 (10 - Sqrt[5]), 10}}],
Polygon[{{0, 30 - Sqrt[5]}, {0, 30}, {20, 20}, {20 - 2 Sqrt[5],
20}, {20 - 2 Sqrt[5], 20}}],
Polygon[{{60, 30}, {60 - 2 Sqrt[5], 30}, {40 - 2 Sqrt[5], 20}, {40,
20}}]}, {EdgeForm[], White,
Polygon[{{25, 0}, {27, 0}, {27, 12}, {0, 12}, {0, 10}, {25, 10}}],
Polygon[{{33, 30}, {35, 30}, {35, 20}, {60, 20}, {60, 18}, {33,
18}}]}, {red,
Polygon[{{27, 0}, {27, 12}, {0, 12}, {0, 18}, {27, 18}, {27,
30}, {33, 30}, {33, 18}, {60, 18}, {60, 12}, {33, 12}, {33,
0}}]}}, PlotRangePadding -> None]
Here's the result:
The war flag has proportion 3:5:
Proportion 1 would look like this:
Once the flag is constructed, it can be manipulated:
and even wilder:
