Area of a regular pentagon with a side of 10in is 172
Step-by-step explanation:
Given:
Side of the regular pentagon = 10in
To Find:
Area of the regular pentagon=?
Solution:
We know that ,
[tex]Area of Pentagon = 5\times\text{ Area of triangle}[/tex]................(1)
Step 1: Finding the Area of the triangle
we know that in a right angle triangle, there are base, height and hypotenuse [tex]tan(\frac{\pi}{5}) =\frac{ height}{hypotenuse }[/tex]
So, from the above equation,
[tex]height=\frac{(base/2)}{tan(36^{\circ})}[/tex]
[tex]height=\frac{5}{tan(36)}=6.88[/tex]
area of right angle triangle
=> [tex]\frac{1}{2}\times base \times height[/tex]
=> [tex]=\frac{1}{2} \times 5\times 6.88[/tex]
=> 17.20
Area of the triangle =2 x area of right angle triangle
Area of the triangle =2 x 17.20
Area of the triangle= 34.40
Step 2: Finding the Area of the pentagon
Substituting the values in (1)
[tex]Area of Pentagon = 5\times 34.40 [/tex]
Area of Pentagon= 172
