Question

The parallel sides of the trapezium are 30 cm and 20 cm. Its non-parallel sides are both equal, each being 13 cm. Find the area of the trapezium.

Answer 1

Answer:

300 cm²

Step-by-step explanation:

Pls find attached the trapezium ABCD with AB=20 ; CD=30 and AC=BD=13cm

To compute the area of the trapezium we need to calculate the height first.

Let's draw 2 perpendiculars AE and BF from AB to CD.

So the figure ABEF is a rectangle. Hence AB=EF=20cm

Also AE=BF.

Now consider the right angled triangles ΔACE and ΔBFD

AC²=AE²+CE² and BD²=BF²+FD²

As AC = BD and AE=BF ; CE=FD=(CD-EF)/2 = 5cm

Hence, 13²=AE²+5²

AE²=169-25=144

AE=12cm

Now we have the height of the trapezium and hence the area will be;

1/2*12*(20+30) = 300