Question

The perimeter of an isosceles trapezium is 134cm and the bases are 54cm and 30cm in length. Find the length of the non-parallel sides of the trapezium and its area.

Answer 1

Perimeter of isosceles trapezium =134cm
Let the non parallel side be x
ATQ
x+x+54+30=134
2x+84=134
2x=134-84
x=50/2
x=25
Now draw a imaginary perpendicular to the base. If trapezium ABCD and perpendicular of both side be M and N, then line segment MN =30cm
DM=CN=54-30/2=24/2=12cm
${a}^{2} + {b}^{2} = {c}^{2} \\ {b}^{2} = {c}^{2} - {a}^{2}$
$b = \sqrt{ {25}^{2} - {12}^{2} } \\ b = \sqrt{(25 - 12)(25+ 12} \\\sqrt{625-144\\ = \sqrt{381} \\ = 19\\ = 36$
Area=1/2(a+b) *h
=1/2(54+30)*19
=47*19
=893cm^2