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s ABD = 1/2 Keliling ABD = 1/2 (4√7 + 8 + 4) = 1/2(4√7 + 12) = 2√7 +6
L ABD = √s(s-AB)(s-BD)(s-DA)
= √(2√7 + 6)(2√7 + 6 - 4√7)(2√7 + 6 - 8)(2√7 + 6 - 4)
= √(2√7 + 6)(6 - 2√7)(2√7 - 2)(2√7 + 2)
= √((6² - 2√7)² )((2√7)² - 2²)
= √(36 - 28)(28 - 4)
= √(8)(24)
= √192
= 8√3 cm²
L BCD = 1/2 (BC)(BD) sin CBD
= 1/2 (12)(8) sin 45°
= 48 (1/2 √2)
= 24√2cm²
L bangun = L ABD + L BCD = (8√3 + 24√2)cm²