Question

In a trapezium non paralle sides are 25cm and 10 cm and parallel sides are 14cm and 13cm find the area of trapeizium

Answer 1

The non-parallel sides of the trapezium are equal - it is an isosceles trapezium. WLG, let us consider the 25 cm side to be the base. The difference in the lengths of the parallel sides is 25−13=12 cm25−13=12 cm. This will be split equally on both sides as the ‘extra’ or extending part of the base.

Now, you’ve got right angled triangles on both the sides, with a hypotenuse of length 10 cm10 cm and a base of 122=6 cm122=6 cm.

From Pythagoras’ Theorem, we can determine the height of the triangle to be 8 cm8 cm. The lengths of the sides are a Pythgorean triplet.

So, the area, ΔΔ is:

Δ=12×8 cm×(25+13) cm