Question

The height of a trapezium shaped field is 28 m. Its parallel sides are 35 m and 14 m. The cows are grazing in
the field tied with a rope of length 3 m. Calculate how much area of the field cannot be grazed by the cows.​

Answer 1

$\sf\bigstar\mid$ Given :

• The height of the trapezium shaped field is 28m.

• The measurement of the two parallel sides are 35m. and 14m. respectively.

• Some cows are grazing in the field along with a rope tied of length 3m.

$\sf\bigstar\mid$ To find :

• The area of the trapezium that cannot be grazed by the cows.

$\sf\bigstar\mid$ Solution :

We know that :

$\gray \bigstar{ \underline{ \boxed{ \sf { \blue{A(area) = \frac{1}{2}h(a + b)}}}}} \gray \bigstar$

Where,

a(length) = 35m.

b(breadth) = 14m.

h(height) = 28m.

Substituting the given values :

$\sf \longmapsto A = \frac{1}{ \cancel 2} \times \cancel{28}(35 + 14)$

$\sf\longmapsto A = 14(49)$

$\green{\bf \longmapsto A = 686 {m}^{2} }$

Now,

• It is told that the length of the rope is 3m. The area which will can be the reached by the cows will be a circular area.(refer to the attachment)

So,

The area that can't be reached by the cows is :

Area of the circle having the radius of 3m.

We know that :

Area of the circle :

$\gray \bigstar{ \underline{ \boxed{\sf { \blue{ A = \pi {r}^{2} }}}}} \gray \bigstar$

Where,

r(radius) = 3m.

Hence,

$\longmapsto \sf A = 3.14 \times {3}^{2}$

$\longmapsto \sf A = 3.14 \times 9$

${ \green{ \longmapsto \sf A = 28.26 {m}^{2} }}$

Therefore,

☯Area that can't be reached by the cows :

➠ Area of the trapezium - Area of the circle

Hence,

$\red \leadsto \sf (686 {m}^{2} -28.26 {m}^{2} )$

$\red \leadsto \sf 657.74 {m}^{2}$

${ \underline{ \boxed{ \orange{ \bf { \therefore \: Required \:\: answer : \red{657.74 m^2} \gray\checkmark}}}}}$

Answer 2

Answer:

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Step-by-step explanation:

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