Question

if the perimeter of trapezium is 64 cm, its non parallel sides are equal to 12 cm each and altitude is 10 cm find the area of trapezium

Answer 1

Let the trapezium be ABCD

Let parallel sides be AB and CD

Therefore non parallel sides be BC and AD that are equal to 12cm

Now,

Perimeters of trapezium = AB + BC + CD + AD

64 = AB + 12 + CD + 12

AB + CD = 64 - 12 -12

AB + CD = 40 -------------------(1)

Now, As given that altitude = 10cm

Area of trapezium =

$\frac{1}{2} \times altitude \times (sum \: of \: parallel \: sides)$

And, From equation 1 we have sum of parallel sides as AB and CD are parallel to each other.

$\frac{1}{2} \times 10 \times 40$

Therefore,

Area of trapezium = 200cm²