Question

5. A playground measures 300 m x 170 m. Find the cost of planting grass on this
at the rate of 80 per hectare.​

Answer 1

SOLUTION :

❖ Given :-

• Measure of the playground is 300 m × 170 m.

Hence, the playground is rectangular in shape.

• Length of the playground, l = 300 m

• Breadth of the playground, b = 170 m

❖ We know that,

$\: \: \boxed{ \sf{ \: Area \: \: of \: \: a \: \: rectangle = Length \times Breadth \: }}$

$\bold{ \therefore \: Area \: \: of \: \: the \: \: playground = l × b } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{= 300 \: m \times 170 \: m} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{= 51000 \: m {}^{2} }$

Again,

$\bigstar \: \: \bold{10000 \: m {}^{2} = 1 \: \: hectare } \\ \\ \bold{ \implies \: 1 m {}^{2} = \frac{1}{10000} \: \: hectare \: } \\ \\ \bold{ \therefore \: 51000 \: m {}^{2} = 5.1 \: \: hectares}$

Hence,

➥ Area of the playground = 5.1 hectares.

Now,

❖ Given that :

$\sf{Cost \: \: of \: \: planting \: \: grass \: \: per \: \: hectare = Rs. \: 80} \\ \\ \sf{ \therefore \: Cost \: \: of \: \: planting \: \: grass \: \: in \: \: 5.1 \: \: hectares = Rs. \: (80 \times 5.1)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{ = Rs. \: 408}$

• The cost of planting grass on the playground measure 300 m × 170 m at the rate of 80 per hectare is Rs. 408.

MORE TO KNOW :

➤ Rectangle :-

A rectangle is a plane figure which has four sides and four angles. Each of the four angles are right angles, i.e, 90°. Again, the opposite sides of a rectangle are of equal length and parallel.

• Area of a rectangle = Length × Breadth

• Perimeter of a rectangle = 2 (Length + Breadth)

➤ Measures :-

• ➛1 hectare = 0.01 square kilometers

• ➛ 1 hectare = 10000 square meters

• ➛ 1 Kilometer = 1000 meters

Answer 2

$\huge \purple{ \underline{ \boxed{ \red{ \mathbb{ANSWER : }}}}}$

$\red{ \textsf{The cost of planting grass on the playground is \orange{Rs.408 .}}}$

$\huge \purple{ \underline{ \boxed{ \red{ \mathbb{EXPLANATION : }}}}}$

$\large\green{ \underline{ \underline{ \mathbb{GIVEN : }}}}$

$\orange{ \textsf{Length of playground = 300 m }}$

$\orange{ \textsf{Breadth of playground = 170 m }}$

$\orange{ \textsf{Cost of planting grass per hectare = Rs.80}}$

$\large\green{ \underline{ \underline{ \mathbb{FORMULA \: USED : }}}}$

$\orange{ \textsf{Area of rectangle = Length x Breadth}}$

$\orange{ \sf{1 \: hectare = 10000 \: {m}^{2} }}$

$\large\green{ \underline{ \underline{ \mathbb{SOLUTION : }}}}$

$\red{ \textsf{Area of playground = Length x Breadth}}$

$\red{ \textsf{Area of playground = 300 x 170}}$

$\red{ \sf{Area \: of \: playground = 51000 \: {m}^{2} }}$

$\red{ \sf{Area \: of \: playground = 5.1 \: hectare }}$

$\red{ \textsf{Cost of planting grass per hectare = Rs.80}}$

$\red{ \sf{Cost \: of \: planting \: grass \: 5.1 \: hectare = 5.1 \times 80}}$

$\red{ \sf{Cost \: of \: planting \: grass \: 5.1 \: hectare = Rs. \: 408 }}$

$\large \green{ \underline{ \underline{ \mathbb{KNOW \: MORE : }}}}$

$\orange{\mathbb{AREA : }}$

The area is the measurement of space enclosed by a closed geometric figure .

$\orange{ \mathbb{HECTARE :}}$

The hectare is a non-SI metric unit of area equal to 10,000 m² .