Asked by Jszca
ABCD is an isosceles trapezoid with AB as its longest side and O divides the diagonals AC and BD in the ratio of 1:2. What is the area of ABCD if the area of BOC is 2 square meter?
Answers
Answered by
MathMate
If AB is the longest side, then O cannot divide AC and BD in the ratio 1:2 since mAB>mDC.
We will use A(BOC) to represent the area of triangle BOC, and so on.
Draw a diagram of the trapezoid ABCD with AB//DC and AB>DC. The diagonals AC and BD meet at O.
If the division is 2:1,
then
A(BOC)=2 (given)
A(COD)=1 (same height, ratio of base)
A(DOA)=2 (congruent with BOC)
A(AOB)=4 (same height as DOA, ratio of sides).
Add up the area of each of the four triangles to get the area of the trapezoid.
We will use A(BOC) to represent the area of triangle BOC, and so on.
Draw a diagram of the trapezoid ABCD with AB//DC and AB>DC. The diagonals AC and BD meet at O.
If the division is 2:1,
then
A(BOC)=2 (given)
A(COD)=1 (same height, ratio of base)
A(DOA)=2 (congruent with BOC)
A(AOB)=4 (same height as DOA, ratio of sides).
Add up the area of each of the four triangles to get the area of the trapezoid.
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