Question

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

Answer 1

Answer:

60 in²

Step-by-step explanation:

Area of a Regular Polygon

  $\textsf{A}=\dfrac{n\:s\:a}{2}$

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:

$\implies \sf A = \dfrac{5 \times 6 \times 4}{2}$

$\implies \sf A = \dfrac{120}{2}$

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

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

Answer 2

$\huge\text{Hey there!}$

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

$\mathbf{\dfrac{1}{2}\times \boxed{a}pothem\times\boxed{p}erimeter = {\boxed{a}rea}}$

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

$\mathbf{\dfrac{\boxed{n}umber\ of\ sides\ you\ have \times \boxed{s}ide \ length\ on\ one\ side\times \boxed{a}pothem}{2} = \boxed{a}rea}$

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

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

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

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

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

$\mathbf{\dfrac{5\times 6 \times 4}{2} = \boxed{a}rea}$

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

$\mathbf{\dfrac{5\times 6 \times 4}{2} = \boxed{a}rea}$

$\mathbf{\dfrac{30\times 4}{2} = \boxed{a}rea}$

$\mathbf{\dfrac{120}{2} =\boxed{a}rea}$

$\mathbf{\dfrac{120\div2}{2\div2} = \boxed{a}rea}$

$\mathbf{\dfrac{60}{1} = \boxed{a}rea}$

$\mathbf{60\div1 = \boxed{a}rea}$

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

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

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

$\huge\text{Good luck on your assingment \& enjoy your day!}$

~$\frak{Amphitrite1040:)}$