+118609 Cut your regular pentagon into 5 isosceles triangles each radiating from the centre.
The cut each of those triangles in half making 10 congruent right angled triangles.
the hypotenuse is the radius of the hypotenuse of the triangles and
One of the sides of the triangle is a half of one side of the pentagon
and the other side of the trianngle is the apothem of the pentagon I am going to call this side $$a$$
The angle radiating from the centre of each right angled triangle is (360/5)/2 = 36 degrees
the length of the side opposite the centre angle is 0.5(240/5) = 24km
Now use tan to get the length of the apothem. you will get $$a\approx 33.03km$$
$$\\Area = 10* $ area of right angled triangle$\\
=10* (0.5*base * height)\\
=10*0.5*24*33.03\\
\approx 3964 km^2$$
+128474 The side must be 240/5 = 48km
We have a "formula" to find the area given the side length....I won't derive it for you, but it is given by:
A = 1.7204 s^2 where s is the side length....so we have
A = 1.7204 (48)^2 = 3963.8 km ^2
+118609 Cut your regular pentagon into 5 isosceles triangles each radiating from the centre.
The cut each of those triangles in half making 10 congruent right angled triangles.
the hypotenuse is the radius of the hypotenuse of the triangles and
One of the sides of the triangle is a half of one side of the pentagon
and the other side of the trianngle is the apothem of the pentagon I am going to call this side $$a$$
The angle radiating from the centre of each right angled triangle is (360/5)/2 = 36 degrees
the length of the side opposite the centre angle is 0.5(240/5) = 24km
Now use tan to get the length of the apothem. you will get $$a\approx 33.03km$$
$$\\Area = 10* $ area of right angled triangle$\\
=10* (0.5*base * height)\\
=10*0.5*24*33.03\\
\approx 3964 km^2$$
