Question

regular pentago ABCDE has a side length of 6square root of 5 cm & area of 309.7 cm square & regular pentagon QRSTU has a side length of 8cm & perimeter of 40cm. Find the perimeter of pentagon ABCDE & area of pentagon QRSTU

Answer 1

both are regular pentagons, so each have 5 equal sides

now, the ABCDE one, has sides with length of 6√(5), well the perimeter of any shape, is all its sides or its borders, added up, so, 5 sides, each 6√(5), then the perimeter of ABCDE is 6√(5)+6√(5)+6√(5)+6√(5)+6√(5) or 5[ 6√(5) ]

now to get the area of pentagon QRSTU, we know it has 5 sides, and each side is 8cm in length

thus
`\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}\cdot n\cdot s^2\cdot cot\left( (180)/(n) \right)\qquad \begin{cases} n=\textit{number of sides}\\ s=\textit{length of one side}\\ (180)/(n)=\textit{angle in degrees}\\ ----------\\ n=5\\ s=8 \end{cases} \\\\\\ A=\cfrac{1}{4}\cdot 5\cdot 8^2\cdot cot\left( (180)/(5) \right)`

now, the angle there is in degrees, thus, make sure your calculator is in Degree mode