Question

the parallel sides of a trapazium are 10cm and 40 cm. If each of the non-parallel side is 25 cm, find the area of the trapazium.​

Answer 1

The trapezium with the parallel sides of 10 cm and 40 cm, and non-parallel sides are 25 cm each is a cyclic quadrilateral. So we can apply Brahmagupta’s formula to find the area as follows:

Total perimeter = 2s = 10+40+25+25 = 100, or s = 50

The area of the figure is thus =[(50–10)(50–40)(50–25)(50–25)]^0.5

= [40*10*25*25]^0.5

= 20*25

= 500 sq cm.

Method 2:

You have two RATs whose hypotenuse = 25 cm and the base = (40–10)/2 = 30/2 = 15 cm.

So the altitude of the RAT = [25^2–15^2]^0.5 = [10*40]^0.5 = 20 cm.

Area of trapezium = (10+40)*20/2 = 50*10

= 500 sq cm.