bonjour
BE² = 12 ² + 6²
BE² = 144 + 36 = 180
BE = √180 = 6 √5
BD² = 3² + 6²
BD² = 9 + 36 = 45
BD = √45 = 3 √ 5
Si BED est rectangle alors
15 ² = ( 6 √5)² + ( 3 √5)²
225 = 180 + 45
225 = 225
donc BED est rectangle
aire BED = ( 3 √5 * 6√5) / 2 = 90 /2 = 45 cm²
aire ABE = ( 12 * 6 ) / 2 = 36 cm²
aire BCD = ( 3 * 6 ) / 2 = 9
aire ABCD = 15 * 6 = 90
donc aire BEC = 90 - 45 = 45 cm²
