Question

The area of a trapezium is 248 sq. m and its height is 8 m. If one of the parallel side
is smaller than the other by 4 m, find two parallel sides.​

Answer 1

Given : Area of trapezium = 248 m² and it's height is 8 m.

One side of trapezium is smaller than the other by 4 m.

Find : Two parallel sides of trapezium.

Solution :

• Let one parallel side be M.

So,

Other side = M - 4

Area of trapezium = $\dfrac{1}{2}$ × (a + b) × h

Here..

"a" and "b" are sides of trapezium.

Put the known values in above formula.

=> 248 = $\dfrac{1}{2}$ × (M + M - 4) × 8 _____ (eq 1)

=> 248 = $\dfrac{1}{2}$ × (2M - 4) × 8

=> 248(2) = (2M - 4)8

=> 496 = 8(2M - 4)

=> $\dfrac{496}{8}$ = 2M - 4

=> 62 = 2M - 4

=> 62 + 4 = 2M

=> 66 = 2M

=> M = 33

So,

• One side of trapezium = 33 m

• Other side of trapezium = 33 - 4 = 29 m

Parallel sides of trapezium are 33 m and 29 m.

☆ VERIFICATION :

From above calculations we have M = 33

Put value of M in (eq 1)

=> 248 = $\dfrac{1}{2}$ × (33 + 33 - 4) × 8

=> 248 = $\dfrac{1}{2}$ × (66 - 4) × 8

=> 248 = $\dfrac{1}{2}$ × (62) × 8

=> 248 = 62 × 4

=> 248 = 248

Answer 2

$\bf{\huge{\underline{\boxed{\tt{\pink{Answer:}}}}}}$

Gívéñ :-

• Area of trapezium = 248 sq.m
• Height of the trapezium = 8 m
• one of the parallel side
• is smaller than the other by 4 m

Tó fíńd :-

• Two parallel sides of the trapezium

Sóĺúťíóń :-

We are given with the area of the trapezium, height of the trapezium and are given the conditions related to the length of the parallel sides of the trapezium.

As per the question,

• One of the parallel sideis smaller than the other by 4 m

Let the length of one of the parallel side be x m = Side 1

•°• Length of the other parallel side is x - 4 m = Side 2

We know that area of a trapezium is given by the formula,

$\bf{\large{\underline{\boxed{\tt{Area\:of\:trapezium\:=\:1/2\:(Sum\:of\:parallel\:sides\:)(height) }}}}}$

Plug the values in the above formula,

248 = $\bf\large\frac{1}{2}$ × ( x + x - 4) (8)

248 × 2 = 8 ( x + x - 4)

496 = 8x + 8x - 32

496 + 32 = 16x

528 = 16x

$\bf\large\frac{528}{16}$ = x

33 = x = Side 1

•°• Length of one of the parallel side = 33 m

Substutite the value of x in the value of other parallel side of the trapezium,

Side 2 = x - 4 = 33 - 4 = 29

•°• Length of two parallel sides of the trapezium are 33m and 29 m, respectively.

$\bf{\huge{\underline{\boxed{\tt{\red{Verification:}}}}}}$

Area of the trapezium = 248 m

Height of the trapezium = 8 m

One parallel side = 33 m

Other parallel = 29 m

Let's plug all these values in the formula of the area of trapezium

248 = $\bf\large\frac{1}{2}$ ( 33 + 29) (8)

248 = $\bf\large\frac{1}{2}$ × 62 × 8

248 = 31 × 8

248 = 248

LHS = RHS

Hence verified.