Question

The parallel sides of a trapezium are 20cm and 30cm and its non parellel sides are 6cm and 8cm. Find area of trapezium.

Answer 1

hope it will help you....

Answer 2

Answer: The answer is 144 cm².

Step-by-step explanation:  As shown in the attached figure, ABCD is a trapezium with AB = 20 cm, CD = 30 cm, AD = 6 cm and BC = 8 cm.

We are to find the area of the trapezium.

The side BE is drawn parallel to AD so that ABED is a parallelogram. Also, in ΔBEC, BE = 6 cm, EC = 10 cm and BC = 8 cm.

So,

$s=\dfrac{BE+EC+BC}{2}=\dfrac{6+10+8}{2}=12~\textup{cm}.$

Therefore, the area of ΔBEC is

$\triangle=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{12(12-6)(12-10)(12-8)}=24~\textup{cm}^2.$

We know that

$\triangle=\dfrac{1}{2}\times BF\times EC\\\\\Rightarrow 24=\dfrac{1}{2}\times BF\times 10\\\\\Rightarrow BF=4.8.$

The area of the parallelogram ABED will be

$A=\dfrac{1}{2}(AB+CD)\times BF=\dfrac{1}{2}(20+30)\times 4.8=25\times 4.8=120~\textup{cm}^2.$

Thus, the area of the trapezium ABCD = Δ + A = 24 + 120 = 144 cm².