Question

find the area of the regular polygon(this is as far as i can go, but now i’m confused again! please help)

Answer 1

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

`Area=(1)/(2)* p* a`

where p is the perimeter

a is the apothem

STEP 3: Calculate the perimeter

`\begin{gathered} Perimeter=side=length* number\text{ of sides} \\ Perimeter=10*42=420cm \end{gathered}`

STEP 4: Calculate the apothem

`\begin{gathered} a=(s)/(2\tan((180)/(n))) \\ a=(42)/(2\tan((180)/(10))) \\ a=(42)/(2\tan(18))=(42)/(0.64983992)=64.63135428 \end{gathered}`

STEP 5: Calculate the area

`\begin{gathered} Area=(1)/(2)*420*64.63135428 \\ Area=210*64.63135428=13572.5844cm^2 \\ Area\approx13572.6cm^2 \end{gathered}`

Hence, the area of the given polygon is approximately 13572.6cm²