Question

Area= in2
Help me please!! Thank you so much

Answer 1

`\huge\text{Hey there!}`

`\huge\textbf{First thing, let's get the formula for}\\\huge\textbf{the regular pentagon/polygon.}`

`\mathbf{(1)/(2)* \boxed{a}pothem*\boxed{p}erimeter = {\boxed{a}rea}}`

`\huge\textbf{Or we could simply say....}`

`\mathbf{\frac{\boxed{n}umber\ of\ sides\ you\ have * \boxed{s}ide \ length\ on\ one\ side* \boxed{a}pothem}{2} = \boxed{a}rea}`

`\huge\textbf{Let's plug the pieces to the equation,}\\\huge\textbf{since we have that information out the}\\\huge\textbf{way.}`

`\bullet\mathbf{\ Number\ of\ sides \rightarrow \boxed{\bf 5}}`

`\bullet\mathbf{\ Side\ length\ of\ one\ side \rightarrow \boxed{\bf 6\ inches}}`

`\bullet\mathbf{\ Apothem \rightarrow \boxed{\bf 4\ inches}}`

`\huge\textbf{Making the equation for you:}`

`\mathbf{(5* 6 * 4)/(2) = \boxed{a}rea}`

`\huge\textbf{Solving for the result:}`

`\mathbf{(5* 6 * 4)/(2) = \boxed{a}rea}`

`\mathbf{(30* 4)/(2) = \boxed{a}rea}`

`\mathbf{(120)/(2) =\boxed{a}rea}`

`\mathbf{(120/2)/(2/2) = \boxed{a}rea}`

`\mathbf{(60)/(1) = \boxed{a}rea}`

`\mathbf{60/1 = \boxed{a}rea}`

`\mathbf{60 = \boxed{a}rea}`

`\huge\textbf{Met the result....}`

`\huge\text{Thus, your answer should be: \boxed{\mathsf{60\ in^2}}}\huge\checkmark`

~
`\frak{Amphitrite1040:)}`

Answer 2

60 in²

Explanation:

Area of a Regular Polygon

`\textsf{A}=(n\:s\:a)/(2)`

where:

• A = area
• n = number of sides
• s = length of one side
• a = apothem (the line drawn from the center of any polygon to the midpoint of one of the sides)

From inspection of the diagram:

• n = 5
• s = 6 in
• a = 4 in

Substitute the values into the formula and solve for A:

`\implies \sf A = (5 * 6 * 4)/(2)`

`\implies \sf A = (120)/(2)`

`\implies \sf A = 60\:in^2`

Therefore, the area of the given regular pentagon IJKLM is 60 in².