Question

The area of trapezium is 248sq.m and its height is 8 m.If one of the parallel side is smaller than the other by 4 m,find two sides.

Answer 1

ANSWER:-

Given:

The area of trapezium is 248m² and its height is 8m. It one of the parallel side is smaller than the other by 4m.

To find:

The two sides of the trapezium.

Explanation:

We have,

• Area of trapezium= 248m²
• Height of the trapezium= 8m

A/q

Let the length of one of the parallel side be R m

Let the length of other parallel side be (R- 4)m

We know that formula of the area of trapezium:

$=\frac{1}{2} *(sum\:of\:base)*height$

$=\:\frac{1}{2} *(R+R-4)*8=248\\\\=\:\frac{1}{2} (2R-4)*8=248\\\\=\:1(2R-4)4=248\\\\=\:(2R-4)=\frac{248}{4} \\\\=\:2R-4= 62\\\\=\:2R=62+4\\\\=\:2R=66\\\\=\:R=\frac{66}{2} \\\\=\:R=33m$

Thus,

The length of one of the parallel side,R= 33m

The length of other of the parallel side, (33-4)m= 29m.

Answer 2

Answer:

$\large\bold\red{33\:m\;and\;29\:m}$

Step-by-step explanation:

Given,

• Area of trapezium , A = 248 sq. m
• Height, h = 8 m

Let one of the parallel sides be x

Therefore,

The other parallel side will be (x -4) m

Now,

We know that,

Area of trapezium is given by formula:

$\large\boxed{\purple{\frac{1}{2}\times(Sum\:of\:parallel\:sides)\times(h)}}$

Therefore,

We get,

$= > \frac{1}{ \cancel{2}} \times (x + x - 4) \times \cancel{8} = 248 \\ \\ = >4( 2x - 4 )= 248 \\ \\ = > 2x - 4 = \frac{248}{4} \\ \\ = > 2x - 4 = 62 \\ \\ = > 2x = 62 + 4 \\ \\ = > 2x = 66 \\ \\ = x = \frac{66}{2} \\ \\ = > x = 33$

Hence,

One parallel side = 33 m

Another parallel side = 29 m