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

903 sq. cm.

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* height`

`A_1=51* 13`

`A_1=663`

Using heron's formula, area of triangle is

`A=√(s(s-a)(s-b)(s-c))`

where,
`s=(a+b+c)/(2)`.

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

`s=(13+37+40)/(2)=45`

Area of triangle is

`A=√(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.