Trapezium problem?

Question

From the intersection of the two diagonals of a trapezium, are created two triangles with a line in the bases of the trapezium. If the areas of these two triangles are A1 and A2, prove that the area
of the trapezium is: A= (√S1 + √S2)^2.
(√- root quadrant)

Sorry, I typed it wrongly, it is:
A= (√A1 + √A2)^2 and not
A= (√S1 + √S2)^2.

Answer 1

A
= (1/2)(B1+B2)(H1+H2), where B is the base length and H is the height
= (1/2)(B1H1+B2H2)
+(1/2)(B1H2+B2H1)
= A1+A2
+(1/2)[2√(A1*A2)+2√(A1*A2)]
= A1+A2+2√(A1*A2)
= (√A1 + √A2)^2
------------------
More explanations:
A1/A2 = (B1/B2)^2
B1 = B2√(A1/A2)

B1H2
=B2H2√(A1/A2)
=2A2√(A1/A2)
=2√(A1*A2)

In the same way, we can prove
B2H1
=2√(A1*A2)

Answer 2

You're getting no answers because your question is inarticulate. If by trapezium you mean what Americans call a trapezoid, the intersecting diagonals create 8 triangles of different sizes, and you must be more specific about which you mean. What does "with a line in the bases" mean? What are S1 and S2? Why aren't A1 and A2 part of the formula for the area if that's all the information we're given?

Answer 3

Here's a hint ;)
Draw a sketch of a trapezium, and mark everything that is mentioned in the problem. (notice where and how the diagonales intersect) If you look at the sketch, you will notice that the trapezium is made out of four triangles. Mark the sides a, b, c, d, and mark the diagonales e and f. Calculate each of the triangle's area by using Heron's formula (you can find it on Wikipedia, for example), then sum all those areas up, and you get the area of the trapezium.

Since you had to calculate A1 and A2 in order to calculate A, try to put A1 and A2 in the formula which is in the original problem, and see what you get.

Good luck.