How do you find the height of a trapezoid?

How do you find the perimeter of an isosceles trapezoid when one of its parallel sides is 6cm greater than its other parallel side and has a height of 4cm with an area of 34cm?

• Answer:

  First find the lengths of the parallel sides and let the parallel sides be x+6 and x: 1/2*(x+6+x)*4 = 34 sq cm Multiply both sides by 2 and then divide both sides by 4: 2x+6 = 17 Subtract 6 from both sides and then divide both sides by 2 to to find the value of x: x = 5.5 Therefore the parallel sides are: 5.5cm and 11.5cm Each side of the trapezoid will have a right angle triangle with a base of 3 and a height of 4 and by usiing Pythagoras' theorem each hypotenuse works out as 5cm So the perimeter is: 5.5+11.5+5+5 = 27cm