Question

Two crossroads, each of width 4 m, runs at right angles through the centre of a rectangular park of length 70 m and breadth 45 m and parallel to the sides of the rectangle. Find the area of the road.​

Answer 1

Answer ::

The area of road is 444m².

Step-by-step explanation ::

To Find :-

• The area of the road.

Solution :-

Given that,

• Two crossroads, each of width 4 m, runs at right angles through the centre of a rectangular park.
• Length of the park = 70m
• Breadth of the park = 45m

ACCORDING THE QUESTION,

The area of first road [ 70m ] :-

⟾ 70 × 4

⟾ 280m²

The area of second road [ 45m ] :-

⟾ 45 × 4

⟾ 180m²

As it is given that, each of width 4 m, runs at right angles through the centre of a rectangular park

Therefore, the area of center of the park,

⟾ 4 × 4

⟾ 16m²

As we know that,

Area of roads = Area of two cross road - Actual area

⟾ Area of roads = ( 280m² + 180m² ) - 16m²

⟾ Area of roads = 460m² - 16m²

⟾ Area of roads = 444m²

The area of road is 444m².

Answer 2

Answer :-

• The area of the roads = 444 m².

Given :-

• Width of the crossroads = 4 m.
• They run at right angles.
• The park is of rectangular shape.
• Length of the park = 70 m.
• Breadth of the park = 45 m.

To find :-

• The area of the roads.

Step-by-step explanation :-

• First we will find the area of the two roads.

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Area of the first road :-

Here,

• Length of the road = 70 m.

• Breadth of the road = 4 m.

We know that :-

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

Therefore,

$\tt Area \: of \: the \:1st\: road = 70 \times 4$

$\overline{\boxed{\tt Area \: of\:the \: 1st \: road = 280}}$

• Area of the first road is 280 m².

Area of the second road :-

• Length of the road = 45 m.

• Breadth of the road = 45 m.

As given above,

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

Therefore,

$\tt Area\: of \:the \:2nd\: road = 45 \times 4$

$\overline{\boxed{\tt Area \:of \:the\: 2nd \: road = 180}}$

• Area of the second road is 180 m².

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• Now, we have the area of the 2 roads. Since
• Since there are crossroads, therefore they must have a common point.

• The common point of the crossroads will always be a square since they cut each other at right angles. So let's find it's area.

We know that :-

$\underline{\boxed{\sf Area \:of \:a \:square = Side \times Side.}}$

Here,

• Side = 4 m.

Therefore,

$\tt Area \:of \:the\: square = 4 \times4$

$\overline{\boxed{\tt Area \:of \:the\: square = 16}}$

Area of the common point is 16 m².

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Now, we have :-

• Area of the roads is :-

Area of the 1st road + Area of the 2nd road - Common point's area.

Here,

• Area of the 1st road = 280 sq.m

• Area of the 2nd road = 180 sq.m

• Area of the common point = 16 sq.m

Thus,

$\sf Area \: of \: the\: roads = 280 + 180- 16$

$\sf Area \: of\: the \:roads = 460 - 16$

$\underline{\boxed{\sf Area \: of\: the \:roads = 444}}$

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• So, the area of the cross roads running through the centre of the rectangular park = 444 m².