Question

If the perimeter of a trapezium be 52 cm , its non- parallel sides are equal to 10 cm each and it's altitudes is 8cm , find the area of the trapezium.

Answer 1

Hey ....
The perimeter is 52 cm
and the altitudes are 8cm
the non parallel sides are 10 cm each

So.. If u look at the triangles formed due to the altitudes .. u will see that their hypotenuses are 10 cm and one side is 8 cm so the other side will be 6 cm by pythagoras theorem

now look at the parallel sides
Amongst them the longer side has 3 parts one is 6 cm second is the upper side and third is also 6 cm ( If u are confused I have attached the figure with this answer) So now the perimeter is 52 cm
10 + 10 + 6 + 6 + 2 ( the upper side)
By calculation the upper side is 10 cm and the lower parallel side is 22 cm

So the area is 1/2 × (10 + 22) × 8
= 128 cm^2

Hope this helps...