Question

ABCD is a trapezium in which AB॥ DC, AB=78cm, CD=52cm, AD= 28cm, and BC=30. Find the area of trapezium.

Answer 1

In trap.ABCD construct a line parallel to AD = 28cm at AB at point E . Than EB= AB-AE = 78-52=26cm.
In ∆ CEB
EC=28cm,CB=30cm&EB=26cm.
S= (28+30+26)/2=42cm.
Area of ∆=√s (s-a)(s-b)(s-c)
√42(42-28)(42-30)(42-26)
√42*14*12*16
√7*6*7*2*2*6*4*4
7*6*2*4
336cm.
Area of ∆= b*h/2
b*h/2=336
b*h=336*2
26*h=336*2 (EB=b=26)
h=336*2/26
H=(168*2/13)cm
Area of trap.= (sum of || sides)*h/2
((52+78)*168*2/13)/2
(130*168*2/13*2)
1680sq.cm