The perimeter of an isosceles trapezium is 134 cm and the bases are 54 cm and 30 cm in length.find the length of nonparallel sides of the trapezium and its area.

Answer 1

the unknown sides are equal, say x. So,

54+x+30+x = 134

If you draw your trapezium and mark off the interior 30x30 square, you will find a right triangle at each end, with base 12 and hypotenuse x.

So, the height of the trapezium is √(x^2-144) making the area

A = (30+54)/2 √(x^2-144)