Math, asked by Mayurkantmishra4909, 1 year ago

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

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Answered by Anonymous
51
\mathfrak{\huge{Your\:Complete\:Question:}}

A field is in the shape of a trapezium whose parallel sides are 25m and 10m and non parallel sides are 14m and 13m find the area of the whole field.

Refer the pic attached for figure.

\mathfrak{\huge{Answer:}}

\mathbb{GIVEN}

A trapezium whose || sides are 10 m and 25 m

The non-parallel sides are 13 m and 14 m

\mathbb{TO\:FIND}

The Area of the trapezium

\mathbb{METHOD}

¤Refer the pic for the construction done.

Due to the construction, we will have one \mathfrak{||^{gm}} and one \mathfrak{\triangle}. We can easily find the areas separately.

Since we aren't provided with the height, we will use the Heron's Formula:

\sf{Area\:of\:\triangle = \sqrt{s(s-a)(s-b)(s-c)}}\\

s = Semiperimeter = \sf{\frac{13+14+15}{2}}\\

s = 21 m

=》 \sf{\sqrt{21(21-13)(21-14)(21-15)}}

=》 \sf{\sqrt{21(8)(7)(6)}}

=》 \sf{84 m^{2}}

Height of the triangle = \sf{\frac{Area \times 2}{b}}\\

Height of the triangle = 11.2 m

Height of the triangle and the parallelogram will be the same.

\sf{Area\:of\:||^{gm}} = b × h

=》 10 × 11.2

=》 \sf{Area\:of\:||^{gm}= 112 m^{2}}

Area of the trapezium = \sf{84 m^{2} + 112 m^{2}}

\sf{Area\:of\:trapezium = 196 m^{2}}

That's your answer ! \huge{\tt{196 m^{2}}}
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Answered by RudrakshRay
5

Ⓐⓝⓢⓦⓔⓡ

A field is in the shape of a trapezium whose parallel sides are 25m and 10m and non parallel sides are 14m and 13m find the area of the whole field.

Refer the pic attached for figure.

GIVEN

A trapezium whose || sides are 10 m and 25 m

The non-parallel sides are 13 m and 14 m

The Area of the trapezieum

Due to the construction, we will have one areas separately.

Since we aren't provided with the height, we will use the Heron's Formula:

Areaof△=

s(s−a)(s−b)(s−c)

s = Semiperimeter =

2

13+14+15

s = 21 m

=》 {\sqrt{21(21-13)(21-14)(21-15)}}

21(21−13)(21−14)(21−15)

=》 {\sqrt{21(8)(7)(6)}}

21(8)(7)(6)

=》 84m

Height of the triangle =

Area×2

Height of the triangle = 11.2 m

Height of the triangle and the parallelogram will be the same.

}Areaof∣∣

gm

= b × h

=》 10 × 11.2

=》Areaof∣∣

gm

=112m

Area of the trapezium = \sf{84 m^{2} + 112 m^{2}}84m

2

+112

Areaoftrapezium=196m

ℏ✺℘ḙ !т ℏḙℓ℘

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