I think it is two triangles and a square or just two triangles and since these both equal up to squares, then how come we have the one half?
2006-12-15 08:41:22 · 9 answers · asked by sherlogenius 2 in Science & Mathematics ➔ Mathematics
Please make it easy to understand. I'm no genius.
2006-12-15 10:32:10 · update #1
it is divided into two triangles
area of triangle 1=1/2l1*h
area of triangle 2=1/2l2*h
adding 1/2(l1+l2)h
where l1 and l2 are the parallel side and h the distance between the
2006-12-15 08:46:12 · answer #1 · answered by raj 7 · 0⤊ 0⤋
The 1/2 comes in because you ar taking the average of the two parallel bases. It is the average of the two bases times the height that gives the area.
This is easily proven by viewing the trapezoid as two triangles and a rectangle. Draw a picture and you will see that the base of the trapezoid is comprised of 3 parts a,b,and c. a is the bases of the left triangle, bis the base of the middle rectangle and c is the bas of the right triangle. b is also the upper base of the trapezoid.
So total area ah/2 +bh + ch/2 =
ah/2 + 2bh/2 +ch/2 =(a+b+c +b)h/2
and since a+b+c =lower base (call it b') we get
A = (b' +b)h/2
2006-12-15 17:08:12 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
The area of a trapezoid is generally given as
(1/2)(a + b)h, where
a = length of upper parallel
b = length of lower parallel
h = altitude, or height
(1/2)(a + b) is the average length of the bases.
Another way of looking at it is that If you divide the trapezoid in half by a line parallel to the bases through the midpoint of the altitude, and "flip" the top one over and end-for-end, matching it to either end, you have a parallelogram with length (a + b) and a height of h/2, the area of which is
(a + b)h/2.
2006-12-15 17:06:09 · answer #3 · answered by Helmut 7 · 0⤊ 0⤋
Area of a triangle is 1/2 bh
Area of a parallelagram is bh
area of a trapazoid is h(b1+b2)/2
take the limits. If b1=b2, you have a parallelagram. (b1+b2)=2b
2b/2=b so toy get A=bh for a parallelagram.
If b1=0, the Area is 1/2 bh which is correct for the triangle you now have.
2006-12-15 17:58:33 · answer #4 · answered by yupchagee 7 · 0⤊ 0⤋
Well, the area = 1/2(sum of parallel sides lengths)height
So, the sum of parallel sides adds more which needs to be cut in half to offset the increase in the length of the modified parallel side.
2006-12-15 16:46:20 · answer #5 · answered by mulla sadra 3 · 0⤊ 0⤋
because the area of a triangles will only necessarily add up to a square if they are equilatteral......and that is not necessarily true in a trapezoid.
2006-12-15 16:45:02 · answer #6 · answered by smartmitch 4 · 0⤊ 0⤋
Average of the two parallel lengths.
2006-12-15 16:46:22 · answer #7 · answered by Bao L 3 · 0⤊ 0⤋
area of a trapezoid
A=h(b1+b2)/2
2006-12-16 11:37:12 · answer #8 · answered by ♥KiYa♥ 3 · 0⤊ 0⤋
we dont answer homework questions on Friday
2006-12-15 16:43:54 · answer #9 · answered by diva 6 · 0⤊ 1⤋