Question

The parallel sides of a trapezium are 24 cm and 20 cm. The distance between them is 7 cm. Find the radius of a circle whose area is equal to the area of the trapezium.
​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

$\:\:$

• The parallel sides of a trapezium are 24 cm and 20 cm

• The distance between them is 7 cm

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

$\:\:$

• The radius of a circle whose area is equal to the area of the trapezium

$\:\:$

$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

$\:\:$

We know that ,

$\:\:$

$\underline{ \underline{\bold{\texttt{Area of trapezium :}}}}$

$\:\:$

➠ $\sf \dfrac { 1 } { 2 } \times (a + b) \times h$ ⚊⚊⚊⚊ ⓵

$\:\:$

Where ,

$\:\:$

• a = 1st Parallel side

• b = 2nd Parallel side

• h = Distance between the parallel sides

$\:\:$

$\underline{ \underline{\bold{\texttt{Area of given trapezium :}}}}$

$\:\:$

• a = 24 cm

• b = 20 cm

• h = 7 cm

$\:\:$

⟮ Putting the above values in ⓵ ⟯

$\:\:$

: ➜ $\sf \dfrac { 1 } { 2 } \times (24 + 20) \times 7$

$\:\:$

: ➜ $\sf \dfrac { 1 } { 2 } \times 44 \times 7$

$\:\:$

: ➜ $\sf 22 \times 7$

$\:\:$

: : ➨ 154 sq. cm. ⚊⚊⚊⚊ ⓶

$\:\:$

• Hence the area of trapezium is 154 sq. cm.

$\:\:$

Now ,

$\:\:$

$\underline{ \underline{\bold{\texttt{Area of circle :}}}}$

$\:\:$

➠ πr² ⚊⚊⚊⚊ ⓷

$\:\:$

Where,

$\:\:$

• r = Radius of circle

$\:\:$

As we need to find the radius of a circle whose area is equal to the area of the trapezium thus we will equate equation ⓶ & ⓷

$\:\:$

So,

$\:\:$

: ➜ 154 = πr²

$\:\:$

: ➜ $\sf 154 = \dfrac { 22 } { 7 } \times r ^2$

$\:\:$

: ➜ $\sf \dfrac { 154 \times 7 } { 22 } = r ^2$

$\:\:$

: ➜ $\sf 7 \times 7 = r ^2$

$\:\:$

: ➜ $\sf r = \sqrt { 7 \times 7 }$

$\:\:$

: : ➨ r = 7 cm

$\:\:$

• Hence the radius of a circle whose area is equal to the area of the trapezium is 7 cm

Answer 2

hope it helps you!!

please mark as brainliest and follow me on brainly!!