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

Answer 1

$\mathfrak{\huge{Your\:Complete\:Question:}}$

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 ! $\huge{\tt{196 m^{2}}}$

Answer 2

Ⓐⓝⓢⓦⓔⓡ

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℘