SOLUTION: 2 trapezoid questions what is the sq feet of the following side 1 base 81 inches side 2 h 82 inches side 3 h 58 inches side 4 angle wall 72 inches side 1 base 77 i

Question 1436: 2 trapezoid questions what is the sq feet of the following
side 1 base 81 inches
side 2 h 82 inches
side 3 h 58 inches
side 4 angle wall 72 inches

side 1 base 77 inches
side 2 h 36 inches
side 3 h 32 inches
side 4 angle wall 72 inches
thx
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
Given trapezoid ABCD as below:
Let a = CD , b = DB , c = AB, d = AC
A B
-----------
/| |\
d / | | \ b
/ | | \
-----------------
C G H D
Or Let AG, GH(height) perp to CD
area of trapezoid ABCD = area of AGHB + area ACG + Area BGD
= AG * AB + 1/2 AG * (CD-AB)
[ use the formula of the area of triangle for 3 side, we have)
= (a+c)* sqrt((a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d))/(4(a-c))

Case (i) CD(a) =81, AC(d) = 82, BD(b) =58, AB(c) = 72.
a-c = 9, but d - b = 82-58 = 24 > 9
( so ACG & BDH form an illegal triangle) and so ABCD is an
illegal trapezoid,no area.

Case (ii) CD(a) = 77, AC(d) = 36, BD(b) =32, AB(c) = 72.
a-c = 5, but d - b = 36- 32 = 4 < 9 (OK)

Area of the trapezoid ABCD = [(77+72)/(4(77-72)]*
sqrt((77+32-72+36)(77-32-72+36)(77+32-72-36)(-77+32+72+36))
= 1515.69 .... answer
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