Question

the area of trapezium is 164 cm² the distance between parrellel sides is 8 cm one parrellel side is 10 cm find the pther​

Answer 1

Answer:

31

Step-by-step explanation:

1/2h (a+b)=164

1/2*8(10+b)=164

10+ b=164/4

b=31

Answer 2

Given

Area of trapezium is 164cm²

Distance between the parallel sides is 8cm

Length of one side is 10cm

To find

Length of other parallel side

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Area of parallelogram=

$\sf \dfrac{1}{2} \times (sum \: of \: its \: parallel \: side) \times height$

Here, distance between the parallel sides is 8cm which would be consider as height of the trapezium.

Now,put the values in the formula :

one side is 10cm

let us assume that other side of trapezium be 'x'cm

Area of trapezium =

$\sf \longmapsto \dfrac{1}{2} \times (10 + x) \times 8$

$\sf \longmapsto \dfrac{1}{2} \times( 80 + 8x )= 164$

$\sf \longmapsto \: 40 + 4x = 164$

$\sf \longmapsto4x = 164 - 40$

$\sf \longmapsto4x = 124$

$\sf \longmapsto \: x = \dfrac{124}{4} = 31$

∴The length of other side is $\bold{\red{31cm}}$

And length of other side is 10cm

Now, check

$\sf \longmapsto \: \dfrac{1}{2} \times (31 + 10) \times 8$

$\sf \longmapsto \dfrac{1}{2} \times (41 \times 8)$

$\sf \longmapsto \dfrac{1}{2} \times 328 = 164$