Question

A room 12.5 my long and 10.5 m wide is surrounded by a verandah 2 m wide all around it. find the area occupied by the verandah

Answer 1

Length of the garden = 90m, Width of the garden = 75m, Width of the path around the garden = 5m

Area of rectangle = Length × Width
= 90 m × 75 m = 6750 m2

We know that, 10000m2 = 1 hectare
Hence; 6750 m2 = 6750 ÷ 10000 = 0.675 hectare

Length of the garden with path = 90 m + 5m + 5m = 100 m
Width of the garden with path = 75 m + 5m + 5m = 95 m

Area of the garden with path = Length × Width
= 100 m × 95 m = 9500 m

Now, Area of the path = Area of the garden with path — Area of the garden
= 9500 m2 — 6750 m2 = 2750 m2

Hence, Area of the path = 2750 m2, and area of the garden = 0.675 hectare

Answer 2

Given data : A room 12.5 m long and 10.5 m wide is surrounded by a verandah 2m wide all around it.

To find : The area occupied by the verandah.

Solution : Here, we know that,

• Width of the verandah : 2 m

• Length of the room : 12.5 m

• Breadth of the room : 10.5 m

Now,

➜ Area of the room = length * breadth

➜ Area of the room = 12.5 * 10.5

➜ Area of the room = 131.25 m²

Now, a/c to given data ;

• Length of the room with width of the verandah : 12.5 + 2 * (2) = 12.5 + 4 = 16.5 m

• Breadth of the room with width of the verandah : 10.5 + 2 * (2) = 10.5 + 4 = 14.5 m

Now,

➜ Area of the room with verandah = length * breadth

➜ Area of the room with verandah = 16.5 * 14.5

➜ Area of the room with verandah = 239.25 m²

Now,

➜ Area of the verandah = {Area of the room with verandah} - {Area of the room}

➜ Area of the verandah = 239.25 - 131.25

➜ Area of the verandah = 108 m²

Answer : Hence, area of the verandah is 108 m².