SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Describe the polygon
The given polygon is a decagon with 10 sides. The length of the each side is 42cm.
STEP 2: Write the formula for calculating the area of the polygon
[tex]Area=\frac{1}{2}\times p\times a[/tex]
where p is the perimeter
a is the apothem
STEP 3: Calculate the perimeter
[tex]\begin{gathered} Perimeter=side=length\times number\text{ of sides} \\ Perimeter=10\times42=420cm \end{gathered}[/tex]
STEP 4: Calculate the apothem
[tex]\begin{gathered} a=\frac{s}{2\tan(\frac{180}{n})} \\ a=\frac{42}{2\tan(\frac{180}{10})} \\ a=\frac{42}{2\tan(18)}=\frac{42}{0.64983992}=64.63135428 \end{gathered}[/tex]
STEP 5: Calculate the area
[tex]\begin{gathered} Area=\frac{1}{2}\times420\times64.63135428 \\ Area=210\times64.63135428=13572.5844cm^2 \\ Area\approx13572.6cm^2 \end{gathered}[/tex]
Hence, the area of the given polygon is approximately 13572.6cm²
