Hi, quick question. For any trapezoid ABCD. with diagonals BD and CA and midpoint O , it creates 4 traingles AOB, COD, BOC, AOD, With Area of AOD=a & Area of BOC=b. With this Information how do i find the area of the whole trapezoid?
Now i know that Area of Triangle BOA=COD. But how would i find the areas of those triangles with the given information as well?
Here's a pic
You probably meant centroid here, right?
The way skeeter did it,
I can only consider that he used a as triangle ACD and b as triangle BAC, not the way the graph indicates.
Moreover, that BC is equal to the height of ABC
and AD is equal to the height of ACD. Am I right?
I don't understand how can you use the diagonals to calculate the height and make it a regular trapezoid formula.
?
I am confused also
is the shortest distance from O to base AD
is the shortest distance from O to base BC
let = shortest distance from AD to BC through point O
I was under the impression that the bases were given values along with the given areas a and b ... solve for h_a and h_b in terms of the given areas and the bases and you can derive an expression for the area of the trapezoid.
also, as pointed out by earboth ...
... no way O can be the midpoint of the respective diagonals. That would make ABCD a rectangle or a rhombus.For any trapezoid ABCD. with diagonals BD and CA and midpoint O ,