Question

the parallel sides of trapezium are 77m and 60m and non parallel sides are 25m and 26m . find the area of trapezium??

Answer 1

Hello,
let's look at the figure.
AB=60 m;DF=77 m;AD=25m; BF=26mwe calculate the CF:
CF=DF-CD=77-60=17 m

For ΔBCF,
we calculate the perimeter of triangle
P=BC+BF+CF=25+26+17=68 m
we calculate the  semiperimeter of the triangle:
p=P/2=68/2=34 m
we use the formula of Heron:
At=√p×(p-BC)×(p-BF)×(p-CF);
=√34(34-25)(34-26)(34-17)
=√34×9×8×17=√41616= 204 m²
we calculate the height of triangle:
BE=2At:CF=(2×204):17=408:17=24 m

we calculate the area of Trapezium
A =[(AB+DF)×BE):2=[(60+77)×24]=(137×24):2=3288:2=1644 m²

bye :-)

Answer 2

Answer:

Draw a line BC parallel to AD

Draw a perpendicular line BE on DF

ABCD is a parallelogram.

BC=AD=25 cm

CD=AB=60 cm

CF=77−CD=17cm

For ΔBCF

semiperimeter of triangle=

2

25+26+17

=

2

68

=34

By Heron's Formula of triangle=

s(s−a)(s−b)(s−c)

=

34(34−25)(34−26)(34−17

)

=204cm²

Also, area of ΔBCF=

2

1

×base×height

204=

2

1

BE×CF

204=

2

1

BE×17

BE=408/17

BE=24 cm

Area of Trapezium=

2

1

(AB+DF)×BE

=1/2(60+77)×24

Area=1644cm²