Question

The area of a trapezium is 400 cm2
, the distance between the parallel sides is 16 cm. If one of the
parallel sides is 20 cm, then the length of the other side is ______

Answer 1

Given :-

Area of trapezium = 1 / 2 * h * ( a + b )

Area of trapezium = 400 cm^2

( a and b are the parallel sides of trapezium )

One parallel side ( a ) = 20 cm

Height ( distance between // lines) = 16 cm

To Find :-

The length of other parallel side = ?

Solution :-

Area of trapezium = 1/2 * h * ( a + b)

Put the required values in the formula,

400 = 1/2 * 16 * ( 20 + b )

400 = 8 * ( 20 + b )

400 = 160 + 8b

400 - 160 = 8b

240 = 8b

b = 240/ 8

b = 30

The length of the other side ( b )

= 30cm

Answer 2

${\frak{\purple{\underline{ \: \: \: question \: : }}}}$

To find length of a parallel side of a trapezium

${\frak{\purple{\underline{ \: \: \: solution \: : }}}}$

Given :

• Area of Trapezium = 400 cm²

• Height = 16 cm (distance between the parallel sides)

• One of the parallel sides is 20 cm

${\boxed{\underline{\bf{area \: of \: trapezium = \frac{1}{2} \times (a + b) \times h}}}}$

• a and b is parallel sides

• h = height.

Let's do ::

Let, one of the parallel sides be x,

$\rightarrow \sf \frac{1}{2} \times (a + b) \times h = 400 \: {cm}^{2} \\ \\ \rightarrow \sf \frac{1}{2} \times (20 + b) \times 16 = 400 \\ \\ \rightarrow \sf \: 8 \times (20 + b) = 400 \\ \\ \rightarrow \sf \: 160 + 8b = 400 \\ \\ \rightarrow \sf \: 8b = 400 - 160 \\ \\ \rightarrow \sf 8b \: = 240 \\ \\ \rightarrow\sf \: b \: = \frac{240}{8} \\ \\ {\boxed{\bf{b = 30}}}$

So, the length of other side of trapezium is 30 cm

Let's verify ::

$\sf \: = \frac{1}{2} \times (a + b) \times h \: = 400 \\ =\sf \frac{1}{2} \times (20 + 30) \times 16 = 400 \\ = \sf \frac{1}{2} \times( 50 ) \times 16 = 400\\ \sf \: = \frac{1}{2} \times 800 = 400 \\ \sf \: 400 = 400$

$\bf \: LHS = RHS$

Thus Solved !!