Elementary 2 Mathematical Geometry Knowing the length of the two diagonals and the height of the tra

It is known that the upper bottom AD parallel to the lower bottom BC in the isosceles trapezoidal ABCD, respectively from the point A and the point D to make the trapezoidal two high AE and DF, according to the Pythagorean theorem to find the length of BF and CE, and add them together, that is, BF + CE = (BE+EF+FB) + EF=BC+EF (and because the quadrilateral AEFD is rectangular, so AD=EF) = BC+AD....That is, the sum of the upper and lower bottoms, and then use it to multiply the height to self-solve.

Connect the midpoint of the upper and lower bottoms to get the trapezoidal height, which must pass the intersection of two diagonals. The two diagonals and the upper and lower bases form two isosceles right triangles, and the height of the trapezoid is equal to the sum of the heights of the two isosceles right triangles.

1 2 * high * [under the root chain (a diagonal 2-high 2) + under the root number (b diagonal 2-high 2)], 9, assuming that the two diagonals of the trapezoid are: a, b, the height is h, the upper bottom and the lower bottom are c, d s trapezoidal = 1 2 (c + d) only tremble h and c + d = (a??-h??

b??-h??s trapezoid=1 2 I'm not good at drawing, you can draw a picture and it will be clear, and if you look at it according to my mathematical formula, it will clearly mean defeat.

Done, I hope you are satisfied with me...0,

Make up a congruent ladder to form a parallelogram, the trapezoidal area is half of the area of the parallelogram, there will be a triangle like 5, 12, 13 (one side of the parallelogram and one diagonal line of each of the two trapezoids), 5 2 + 12 2 = 13 2, is a large right triangle, the area is half of the parallelogram brigade, equal to the trapezoidal area of the shed.

So the trapezoidal area is 5*12 2=30

The height of the trapezoid is 12, and the length of the two diagonals is , see the picture.

Pan db to cb', db=cb'=17Because cf is the height of the trapezoid, the Pythagorean theorem gets: af=6 (ac=10, cf=de=8); b'f=15(cb'=17,cf=de=8) so s acb'=trapezoidal adcb=1 2 (ab') cf=21 8 1 2=84

ab‘=af+b’f=21）

Two diagonals can form two right triangles with height, using the Pythagorean theorem to find the other side, the addition of the two sides is the top bottom and the bottom bottom, and then multiply the height by 2 is the find.

Can you send the picture out, I'll take a look!