The area of the inner section is 320 cm^2
The area of the bigger section is 96 cm^2 (bigger trapezoid)
The area of the smaller trapezoid is 80 cm^2
Here, we want to calculate the area of each section of the frame
As we can see, there are 5 sections of the frame
The inner section represented by a rectangle and 4 adjoining shapes looking like a trapezoid
The inner part of the frame is a rectangle that measures 16 cm by 20 cm
Now, for the trapezoid part, we have 2 different sets
The first two set, has a longer length 28 cm, and shorter length of 20 cm
The second set has a longer length of 24 cm and a shorter length of 16 cm
Now, to get the area of the trapezoid, we need the height of the trapezoid which is called the width in this case. This measure corresponds to a measure of 4 cm on the two sets
Mathematically, the area of a trapezoid is;
[tex]A\text{ = }\frac{1}{2}(a\text{ + b)h}[/tex]Where a is the longer length and b is the shorter length with h representing the width of 4 cm
For the bigger trapezoid, we have;
[tex]\frac{1}{2}(28+20)4=96cm^2[/tex]For the smaller trapezoid, we have;
[tex]\frac{1}{2}\times(24_{}+16)\text{ 4 = }80cm^2[/tex]Then, we have the inner section as;
[tex]\begin{gathered} \text{Area = length }\times\text{ width} \\ =\text{ 16 cm }\times20cm=320cm^2 \end{gathered}[/tex]