Question

a field in the shape of a Trapezium whose parallel sides are 25m and 10m the non parallel sides are 14m and 13m find the area of the field

Answer 1

Here's your answer!!

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It's given that,

Length of parallel sides are 25cm and 10cm.

And length of non-parallel sides are 14 cm and 13 cm.

We have to find it's area , to find the area of Trapezium we must have sum of parallel sides and height of Trapezium.

We have parallel sides , but we have to find height.

So,

We will first drawn AE // BC
=> AE =BC= 13 cm

Now,

In ∆ ADE,
=>AD =14 cm (Given)
=>AE =13 cm

And,

=>DE=DC-EC
$= > 25 - 10 \\ = > 15cm$

Therefore,

$= > s = \frac{a + b + c}{2}$

$= > s = \frac{14 + 13 + 15}{2}$

$= > s = \frac{42}{2}$

$= > s = 21$

Therefore,

Area of ∆ADE =

$= > \sqrt{s(s - a)(s - b)(s - c)}$

$= > \sqrt{21(21 - 14)(21 - 13)(21 - 15)}$

$= > \sqrt{21 \times 7 \times 8 \times 6}$

$= > \sqrt{7 \times 3 \times 7 \times 2 \times 2 \times 2 \times 3 \times 2}$

$= > 7 \times 3 \times 2 \times 2$

$= > 84$

Hence,

Area of ∆ ADE = 84 cm^2

$= > \frac{1}{2} \times base \times height = 84 {cm}^{2}$

$= > \frac{1}{2} \times 15 \times height = 84$

So,

$= > height = \frac{84 \times 2}{15}$

$= > height = \frac{168}{15} = \frac{56}{5} = 11.2$
Hence,

Height of Trapezium= 11.2cm

Now, we can easily find the area of Trapezium.

Area of Trapezium=

$= > \frac{1}{2} \times (sum \: of \: parallel \: side) \times height$

$= > \frac{1}{2} \times (10 + 25) \times 11.2$

$= > \frac{1}{2} \times 35 \times 11.2$

$= > 196 \: {cm}^{2}$

Hence,

Area of Trapezium is 196 cm^2

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Hope it helps you!! :)

Answer 2

Given:Length of parallel sides are 25cm and 10cm.

And,

length of non-parallel sides are 14 cm and 13 cm.

To find:  area of Trapezium

Soln: we have to find height.

So,

We will first drawn EC // AB

=> EC =AB= 13 cm

Now,

In ∆ CED,

=>CD =14 cm

=>EC =13 cm

And,

=>ED=AD-AE

= > ED=25-10

= > ED=15cm

Therefore,

= >s=a+b+c/2

= >s=21cm

Therefore,

Area of ∆CED =√{s(s-a)(s-b)(s-c)}

                        = √{21(21-13)(21-14)(21-15)}

                        =   84cm²

So,

     Area of ∆CED  =   84cm²

     1/2  ×  base × height =   84cm²

     1/2  × 15cm  × height =   84cm²

     height  = 11.2cm

Now,

     Area of Trapezium=(sum of parallel side)/2×height

                                    =(25+10)/2×11.2

                                    = 196 cm²