Trapezoid Problem #2

Geometry Level pending

Given a trapezoid ABCD (AB is parallel to CD). AC meets BD at O. Draw a straight line through O which is parallel to AB and meets AD and BC at M and N, respectively.

Given the area of 2 triangles, A O B AOB and C O D COD , are a 2 a^2 and b 2 b^2 , respectively.

Express the area of the trapezoid ABCD by only variables a , b a, b or numbers. Choose the best answer.

1 ( a b ) 2 × ( a 2 + b 2 ) 2 \frac{(ab)^2 \times (a^2+b^2)}{2} a + b + a b a+b+ab ( a + b ) 2 (a+b)^2 a 3 + b 3 2 \frac{a^3+b^3}{2} a 2 + b 2 \sqrt{a^2+b^2} a 3 + b 3 + a 2 b + a b 2 3 \sqrt[3]{a^3+b^3+a^2b+ab^2} None of the iother answers are correct

Tin Le by Tin Le , 15, Vietnam

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