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S_AKM = 1/2 * AK * AM * sinA = 1/2*2c*b*sinA=bc*sinA,
S_KBL = 1/2 * KB * BL *sinB = 1/2 * c * 2a * sinB = ac*sinB
S_LCM = 1/2 * LC * MC * sinC = 1/2 * a * 2b * sinC = ab*sinC
S_AKM + S_KBL + S_LCM = bc*sinA + ac*sinB + ab*sinC = 2
С другой стороны,
S_ABC = 1/2 * AB * AC * sinA = 1/2 * 3c * 3b * sinA = 9/2 * bc*sinA
S_ABC = 1/2 * AB * BC * sinB = 1/2 * 3c * 3a * sinB = 9/2 * ac*sinB
S_ABC = 1/2 * BC * AC * sinC = 1/2 * 3a * 3b * sinC = 9/2 * ab*sinC
Сложим эти три выражения, получим:
3*S_ABC = 9/2 * (bc*sinA + ac*sinB + ab*sinC) = 9/2 * 2 = 9
Отсюда S_ABC = 3
Тогда S_KLM = S_ABC - (S_AKM + S_KBL + S_LCM) = 3 - 2 = 1
ответ: 1.