S BCD= BC*CD/2 = 2*2/2 =2 (см^2)
BD= √(BC^2 +CD^2) = √8 =2√2
p ABD= (AB+AD+BD)/2 = (10+10+2√2)/2 =10+√2
S ABD= √[p(p-AB)(p-AD)(p-BD)] =
= √[(10+√2)(10+√2-10)(10+√2-10)(10+√2-2√2)] =
= √[(10+√2)*2*(10-√2)] = √[(100-2)*2] = 14 (см^2)
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ИЛИ
BD^2 = AB^2 +AD^2 -2*AB*AD*cos(BAD) <=>
<=> cos(BAD)= (AB^2 +AD^2 -BD^2)/2*AB*AD =
= (100+100-8)/2*10*10 = 0,96
sin(BAD)= √[1-cos^2(BAD)] = 0,28
S ABD= AB*AD*sin(BAD)/2 = 100*0,28/2 =14 (см^2)
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S ABCD= S ABD +S BCD = 14+2 =16 (см^2)