Question

the length of two parallel sides of a trapezium are 91 cm and 51 cm and the length of two other side 37 CM and 13 cm respectively determine the area of trapezium​

Answer 1

Answer:

903 sq. cm.

Step-by-step explanation:

It is given that the length of two parallel sides of a trapezium are 91 cm and 51 cm and the length of two other side 37 CM and 13 cm respectively.

Now draw a dotted line as shown in the below figure. So, we have a triangle with sides 13 cm, 37 cm, 40cm and a parallelogram with sides 51 cm, 13 cm.

Area of parallelogram is

$A_1=base\times height$

$A_1=51\times 13$

$A_1=663$

Using heron's formula, area of triangle is

$A=\sqrt{s(s-a)(s-b)(s-c)}$

where, $s=\dfrac{a+b+c}{2}$.

The sides of triangle are 13cm, 37 cm, and 40 cm.

$s=\dfrac{13+37+40}{2}=45$

Area of triangle is

$A=\sqrt{45(45-13)(45-37)(45-40)}=240$

The area of trapezium is

$A=A_1+A_2=663+240=903$

Therefore, the area of trapezium is 903 sq. cm.