Question

the parallel sides of a trapezium are 25 cm and 13 cm it's non parallel sides are equal each being 10cm find the area of the trapezium

Answer 1

See the attached file

Answer 2

SOLUTION

Let PQRS be the given trapezium

in which PQ ║ SR.

                                                   

Draw RX ⊥ PQ and RY ║ SP,

these meeting PQ at X and Y.

                                                   

It is clear that PYRS is a

parallelogram.

                                                   

∴ PY = SR = 13 cm

 YQ = PQ - PY = 25 cm - 13 cm

       = 12 cm

                                                   

Now, RY = SP = 10 cm and RQ = 10 cm

                                                   

∴ ΔRYQ  is an isosceles triangle and

RX ⊥ YQ.

                                                   

Clearly, X is the midpoint of YQ.

∴ XY = XQ = 1/2 × YQ = 1/2 × 12 CM = 6 CM

                                                   

In ΔRXY, we have

(RX)² = (RY)² - (XY)² (Here we use Pythagoras theorem)

        = (10)² - (6)²

        = 100 - 36

        = 64

⇒ RX = 8 cm

                                                   

Area of the trapezium PQRS

= 1/2 × (25+13) × 8

= 152 cm²