Question

Find the area of trapezium whose parallel sides are 77cm and 60cm and the other sides are 25cm and 26cm

Answer 1

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Answer 2

Answer:

$\text{The area of trapezium is }1644 cm^2$

Step-by-step explanation:

Given a trapezium whose parallel sides are 77 cm and 60 cm and the other sides are 25 cm and 26 cm.

we have to find the area of trapezium.

AD=60 cm

BD=77 cm

AB=25 cm

DC=26 cm

EC=BC-BE=77-60=17 cm

In triangle DEC

$Semiperimeter=\frac{17+26+25}{2}=\frac{68}{2}=34$

By Heron's formula,

Area of triangle DEC can be calculated as

$Area=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{34(34-25)(34-26)(34-17)}$

$Area=\sqrt{34\times 9\times 8\times 17}$

$Area=\sqrt{41616}=204cm^2$

$\frac{1}{2}\times base\times height=204$

$\frac{1}{2}\times 17\times h=204$

$h=24 cm$

Now, area of trapezium can be calculated as

$\frac{1}{2}\times (\text{sum of parallel sides})\times height$

$=\frac{1}{2}\times (77+60)\times 24$

$=1644 cm^2$

$\text{The area of trapezium is }1644 cm^2$