Answer:
451.2(see the attachment)
Step-by-step explanation:
to find the area,you divide the polygon into 5 congruent isosceles triangles.
then calculate the vertex angle
all vertex angle together make 360⁰,and all of them are equal,so each vertex angle=
[tex] \frac{360}{5} = 72[/tex]
draw a perpendicular from one of the vertex angle in one triangle,so it divides 72 in 36⁰ and 36⁰,calculate the other two angles in the triangle,it is isosceles,assume the other angle as x.
[tex]72 + x + x = 180 \\ 72 + 2x = 180 \\ 2x = 108 \\ x = 54[/tex]
now,using the knowledge of trigonometry,we learnt in high school,
[tex]tan54 = \frac{perpendicular}{base} [/tex]
since altitude divides the segment into two equal parts each part is 8.1,as shown in the figure.
[tex]perpendicular = 11.14[/tex]
now,use the formula to find area of one triangle,
[tex] \frac{1}{2} \times base \times height \\ = \frac{1}{2} \times 16.2 \times 11.14 \\ = 90.234[/tex]
since,there are 5 triangles in this polygon,
area of all 5 triangles=area of polygon with side 16.2,
[tex] = 90.234 \times 5 = 451.17 \: or \: 451.2(approximately)[/tex]
