Question

The area of trapezium us 91cm2 and its height is 7cm. If one of the
parallel sides is larger than the other side by 8 cm. Find the length of
two parallel sides.​

Answer 1

${\huge{\underline{\underline{\sf{\maltese\; Question:-}}}}}$

Q) The area of trapezium is 91 cm² and it's height is 7 cm . If one parallel side is larger than other side by 8 cm . Find the length of two parallel sides .

${\huge{\underline{\underline{\sf{\maltese \; Answer\checkmark}}}}}$

✯ Concept :

• In these type of Questions , we just simply use the given relation in the Formula of area or perimeter (which is given in the Question) and simply solve it to get the answer .

• In this question , using the given relation between the two parallel sides , we would put it in the Formula Used to find the area of trapezium .

• After solving this , we would get the measures of one side , then we will put it in the given relation , to find the second parallel side .

✯ Given :

• Area of trapezium = 91 cm²
• Height = 7 cm
• One parallel side = 8 + the other parallel side .

✯ To Find :

• The length of the two parallel sides .

✯ Solution :

• Let one parallel side be = x cm
• so , the other parallel side = x + 8 cm

So , Using the Formula to find area :

$\boxed{ \rm \: area = \frac{1}{2} (sum \: of \: parallel \: sides) \times height}$

Put the values here ..

$\mapsto \rm \: \cancel{91} \: \cancel{cm}^{2} = \frac{1}{2} (x + x + 8) \: \cancel{cm} \times \cancel7 \: \cancel{cm}$

$\mapsto \rm \: 13 \: = \frac{1}{2} (2x + 8)$

$\mapsto \rm \: 13 \times 2 = 2x + 8$

$\mapsto \rm \: 26 - 8= 2x$

$\mapsto \rm \: \cancel2x = \cancel{18}$

$\mapsto \boxed{ \rm \: x = 9}$

So ,

• First parallel side = x cm = 9cm
• Second parallel side = x + 8 cm = 9+8 cm = 17 cm

_________________________

✯ More about Trapezium :

• Trapezium is a Quadrilateral i.e. a 4 sided figure.

• In trapezium , one set of sides are parallel .

$\rightarrow\frak{ \: area \: of \: trapezium = \frac{1}{2} (sum \: of \: parallel \: sides) \times height}$

$\rightarrow \frak{perimeter \: of \: trapezium = sum \: of \: all \: sides}$