Question

The area of trapezium is 686 cm square !. If one of the parallel sides exceeds the other by 7cm and the distance between the parallel sides is 28cm, find the other parallel side of the trapezium.

Answer 1

Distance between parallel sides = height of trapezium

Area of trapezium =

2

1

(sum of parallel sides) × height

441=

2

1

(x+28)×18

⇒x+28=49⇒x=21cm

Answer 2

Given:-

• Area of trapezium = 686cm²
• One of the parallel side exceeds other by 7cm.
• Distance between the parallel sides = 28cm

Solution:-

Let the parallel side be x.

So the other parallel side will be (x + 7)cm

We know that,

$\bullet\quad\boxed{\rm Area \ of \ Trapezium = \dfrac{1}{2}(sum \ of \ parallel \ sides)(distance \ between \ parallel \ sides)}$

Hence,

$\rm 686cm^2 = \dfrac{1}{2}[(x+7)cm+x \ cm](28cm)$

$\rm \dashrightarrow 686cm^2 = \dfrac{[(2x +7) cm](28cm)}{2}$

$\rm \dashrightarrow 686cm^2 =(2x+7)cm14cm$

$\rm \dashrightarrow \dfrac{686cm^2}{14cm} =(2x+7)cm$

$\rm \dashrightarrow 49cm =(2x+7)cm$

$\rm \dashrightarrow 49cm - 7cm =2x$

$\rm \dashrightarrow 42cm =2x$

$\rm \dashrightarrow \dfrac{42cm}{2}=x$

$\bf\dashrightarrow x = 21cm$

• Parallel side = x = 21cm

• Other Parallel side = x + 7 = 21 + 7 = 28cm.