Points A and B are the mid points of the sides of the square. Whose length are 8. Find the area of the trapezoid ABCD.

Question

Points A and B are the mid points of the sides of the square Whose
length are 8 Find the area of the trapezoid ABCD

Brijendra Pal · Accepted Answer

Hi,
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Side of square = 8 cm So diagonal = 82 cm Since A is the mid point of EF and AN||EM so N will be mid point of ABSo △FAN~FEMFAEA= FNMNSo FN = MN Now M is the mid point of EG so EM = 42 So FM = 82-422= 42So MN = 22Now AB will be half of EG , using  mid point theorem, AB = 42Now for CD, we can use symmetry property that C and D will be trisection point ofEG so CD = 13EG = 823So area of trapezoid ABCD = 12×AB+CD×MN= 12 42+823× 22= 8+163=403 cm2Regards