Question

the area of a tropezi 41m shoped find is 480m the distance between two paraul side is 15m and one of the paraul side is 20m find other side​

Answer 1

⠀⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Correct~Question}}}}$

The area of a trapezium shaped field is 480m^2, the distance between two parallel sides is 15m and one of the parallel side is 20m . find the other parallel side.

⠀⠀⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Answer}}}}$

Given:

• the area of a trapezium shaped field is 480 m²

• the distance between two parallel sides is 15 m

• one of the parallel side is 20m .

To find:

find the other parallel side.

Solution:

ABCD is a trapezium with parallel sides AB and CD

AB = 20 m and

Let the length of the other parallel side,CD be ' x ' m

Area of the trapezium ( A ) = 480 m²

Height of the trapezium ( h ) = 15 m

We know that ,

$\boxed{\bf{\pink{Area\:of\:trapezium=\dfrac{AB+CD}{2}×h}}}$

Where,

AB + CD = sum of parallel sides

h = height of the trapezium

ATQ,

$\sf{:\implies 480=\dfrac{20+x}{2}×15}$

$\sf{:\implies \dfrac{2×480}{15}=20+x}$

$\sf{:\implies 64=20+x}$

$\sf{:\implies 20+x=64}$

$\sf{:\implies x=64-20}$

$\sf{:\implies x=44}$

$\boxed{\bf{\red{x\:=\:CD\:=44}}}$

Hence,

${\pink{\underline{\underline{\purple{\textsf{\textbf{length\:of\:other\:parallel\:side\:is\:44\:m}}}}}}}$

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Answer 2

$\displaystyle\large\underline{\sf\red{Given}}$

• ✭ Area of a Trapezium is 480 m²

• ✭ Distance between the two parallel sides(height) = 15 m

• ✭ One of the parallel side = 20 m

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

• ◈ The other side?

$\displaystyle\large\underline{\sf\gray{Solution}}$

So we know that area of a Trapezium is given by,

$\displaystyle\sf\underline{\boxed{\sf \dfrac{Sum \ of \ parallel \ sides}{2} \times Height}}$

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$\displaystyle\sf\underline{\boldsymbol{\bullet \: According \ to \ the \ Question}}$

Parallel sides are of length x & 20 m

Height of the figure is 15 m

Area is 480 m²

$\displaystyle\sf\dashrightarrow \dfrac{20+x}{2} \times 15 = 480$

$\displaystyle\sf\dashrightarrow \dfrac{20+x}{2} = \dfrac{480}{15}$

$\displaystyle\sf\dashrightarrow \dfrac{20+x}{2} = 32$

$\displaystyle\sf\dashrightarrow 20+x = 32\times 2$

$\displaystyle\sf\dashrightarrow 20+x = 64$

$\displaystyle\sf\dashrightarrow x = 64-20$

$\displaystyle\sf\pink{\dashrightarrow x = 44 \ m}$

$\displaystyle\sf\therefore The \ other \ parallel \ side \ is \ 44 \ m$

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