<prompt> Acha mathbfp na mathbfq ziwe vivekta viwili vya pande tatu hivi kwamba pembe kati yao ni 30circ. Tafuta eneo la msambamba ambao diagonal zake zinalingana na mathbf p 2 mathbfq na 2 mathbfp mathbfq.  <response>: Tuseme kwamba vekta mathbfa na mathbfb zitoe paralelogramu. Kisha vekta zinazolingana na diagonals ni mathbfa mathbfb na mathbfb - mathbfa.asyukubwa wa kitengo sentimita 0.4;jozi A, B, C, D, trans;A 0,0;B 7,2;C 1,3;D B C;trans 10,0;kuchoraB--D--C;choraA--B,Arrow6;choraA--C,Arrow6;choraA--D,Arrow6;lebomathbfa, A B2, SE;lebomathbfb, A C2, W;lebomathbfa mathbfb, interpA,D,0.7, NW, UnFill;kuchorakuhamatransB--D--C;chorashifttransA--B,Arrow6;chorashifttransA--C,Arrow6;chorashifttransB--C,Arrow6;lebomathbfa, A B2 trans, SE;lebomathbfb, A C2 trans, W;lebomathbfb - mathbfa, B C2 trans, N;asyHivyo,anzaalignmathbfa mathbfb mathbfp 2 mathbfq, mathbfb - mathbfa 2 mathbfp mathbfq.endalignKutatua kwa mathbfa na mathbfb, tunapataanzaalignmathbfa fracmathbfq - mathbfp2, mathbfb frac3 mathbfp 3 mathbfq2.endalignEneo la parallelogramu hutolewa naanzaalignmathbfa nyakati mathbfb kushoto fracmathbfq - mathbfp2 mara frac3 mathbfp 3 mathbfq2 kulia frac34 mathbfq - mathbfp nyakati mathbfp mathbfq frac34 mathbfq nyakati mathbfp mathbfq nyakati mathbfq - mathbfp nyakati mathbfp - mathbfp nyakati mathbfq frac34 -mathbfp nyakati mathbfq mathbf0 - mathbf0 - mathbfp nyakati mathbfq frac34 -2 mathbfp mara mathbfq frac32 mathbfp nyakati mathbfqendalignKwa kuwa mathbfp na mathbfq ni vekta za kitengo, na pembe kati yake ni 30circ,mathbfp nyakati mathbfq mathbfp mathbfq sin 30circ frac12.Kwa hivyo, eneo la parallelogramu ni frac32 cdot frac12 frac3 4. 