We prove that for every
r
>
0
r>0
if a nonpositively curved
(
p
,
q
)
(p,q)
-map
M
M
contains no flat submaps of radius
r
r
, then the area of
M
M
does not exceed
C
r
n
Crn
for some constant
C
C
. This strengthens a theorem of Ivanov and Schupp. We show that an infinite
(
p
,
q
)
(p,q)
-map which tessellates the plane is quasi-isometric to the Euclidean plane if and only if the map contains only finitely many nonflat vertices and faces. We also generalize Ivanov and Schupp’s result to a much larger class of maps, namely to maps with angle functions.