So many colored areas.

Geometry Level 3

Four squares $A$ , $B$ , $C$ , and $D$ are connected to each other with the given dimensions 4, 3, 2, and 1 respectively.

What is the area of the colored region (the area of red, blue, green and yellow combined)?

1 solution

Hana Wehbi
Aug 6, 2018

First we need to find the ratio of proportionality: $\frac{4}{1+2+3+4} =0.4$

Area of Red Region: $\color{#D61F06}\frac{1.6\times 4}{2}=3.2$

Area of Green Region: $\color{#20A900}\frac{(2.4+1.2)(3)}{2}=5.4$

Area of Yellow Region: $\color{#CEBB00}\frac{(1.6+0.8)(2)}{2}=2.4$

Area of Blue Region: $\color{#3D99F6}\frac{1\times 0.4}{2}=0.2$

Thus, the total area is: $3.2+5.4+2.4+0.2=\boxed{11.2}$