Question

The area of a trapezium shaped field is 480m, the distance between two parallel sides is 15m and one of the parallel side is 44m. find the other parallel side.

Answer 1

$\frak{Given}\begin{cases}&\sf{Area\;of\; trapezium = \frak{480\;m^2}}\\&\sf{Distance\;b/w\;||\;sides =\frak{15\;m}}\\&\sf{One\;of\;the\;||\;side =\frak{44\;m}}\end{cases}$

ᴅɪᴀɢʀᴀᴍ :

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❍ Let's say, the other parallel side of the trapezium be x m respectively.

• We'll calculate the other side of the trapezium by using the area's formula of trapezium, the formula is given by :

$\bf{\dag}\;\boxed{\sf{Area_{\:(trapezium)} = \bigg( \dfrac{1}{2} \times (a + b) \times h\bigg)}}$

where,

• a & b is the sum of || sides.
• h is the Height.
• Area is given, that is 480 m².

$\rule{100px}{.3ex}$

C A L C U L A T I N G :

$:\implies\sf 480 = \dfrac{1}{2} \times (44 + x) \times 15 \\\\\\:\implies\sf \dfrac{480 \times 2}{15} = 44 + x\\\\\\:\implies\sf \cancel\dfrac{960}{15} = 44 + x \\\\\\:\implies\sf 64 = 44 + x \\\\\\:\implies\sf x = 64 - 44 \\\\\\:\implies\underline{\boxed{\frak{x = 20}}}$

$\therefore{\underline{\textsf{Hence,\; other\; parallel\: side\; of\; trapezium\;is\; {\textbf{20 m}}.}}}$

Answer 2

Given :

Area of trapezium = 480 m

Distance between parallel side = 15 m

One parallel side = 44 m

To Find :-

Other parallel side

Solution :-

Let the other parallel side be x

As we already know that,

Area = 1/2(a + b) h

a and b are parallel sides

h is the distance between them

480 = 1/2(44 + x) 15

$\sf 480 \times 2 = (44 + x) \times 15$

$\sf 960 = (44 + x) \times 15$

$\sf \dfrac{960}{15} = 44 + x$

$\sf 64 = 44 + x$

$\sf 64 - 44 = x$

$\sf 20 = x$

Hence

• Other parallel side is 20 m