如图，已知△ABC的周长是21，OB，OC分别平分∠ABC和∠ACB，OD⊥BC于D，且OD=3，△ABC的面积是______

作OE⊥AC，OF⊥AB，垂足分别为E、F，连接OA，∵OB，OC分别平分∠ABC和∠ACB，OD⊥BC，∴OD=OE=OF，∴S △ABC =S △OBC +S △OAC +S △OAB = 1 2 ×OD×BC+ 1 2 ×OE×AC+ 1 2 ×OF×AB= 1 2 ×OD×（BC+AC+AB）= 1 2 ×3×21=31.5．故填31.5．