Get points of any regular polygon that can be also rotated

I'm trying to draw any regular polygon, so from triangles to polygons with so many corners, it looks like a circle. to make it easier, they must be regular, so a normal pentagon/hexagon/octagon etc. I want to be able to rotate them. What ive tried is to draw a circle and divide 360 by the amount of points i want then, create a point every nth degrees around the circle, putting these points in pygame.draw.polygon() then creates the shape i want, the problem is it isn't the right size, i also want to be able to have stretch the shapes, so have a different width and height.

def regular_polygon(hapi, x, y, w, h, n, rotation, angle_offset = 0):
    #angle_offset is the starting angle in the circle where rotation is rotating the circle
    #so when its an oval, rotation rotates the oval and angle_offset is where on the oval to start from
    if n < 3:
        n = 3

    midpoint = pygame.Vector2(x + w//2, y + h//2)
    r = sqrt(w**2 + h**2)
    #if angle_offset != 0:
        #w = (w//2)//cos(angle_offset)
    #if angle_offset != 90:
        #h = (h//2)//sin(angle_offset)
    w,h = r,r

    points = []

    for angle in range(0, 360, 360//n):
        angle = radians(angle + angle_offset)
        d = pygame.Vector2(-sin(angle)*w//2, -cos(angle)*h//2).rotate(rotation) #the negative sign is because it was drawing upside down

        points.append(midpoint + d)
    #draws the circle for debugging
    for angle in range(0, 360, 1):
        angle = radians(angle + angle_offset)
        d = pygame.Vector2(-sin(angle)*w//2, -cos(angle)*h//2).rotate(rotation)
        pygame.draw.rect(screen, (0,255,0), (midpoint[0] + d[0], midpoint[1] + d[1], 5, 5))

    pygame.draw.polygon(screen,(255,0,0),points)

enter image description here

the red square is the the function above is making, the blue one behind is what it should be

as you can see the circle does line up with the edges of the rect, but because the angles of the circle are not even, the rectangle the func makes is not right.

i think i need to change the circle to an oval but cannot find out how to find the width radius and height radius of it. currently ive found the radius by using pythag.

this is what happens when i dont change the width or height

enter image description here