Question

The diagram represents the floor of a room. All dimensions are in metres and all the angles are right angles. Calculate

1. the perimeter of the room
2. the area of the floor
3. the volume of the room if it is 3 m high.

Answer 1

We have,

The diagram represents the floor of a room. All dimensions are in metres and all the angles are right angles. Calculate the perimeter of the room

Now we know that,

i. The perimeter of a polygon is the sum of all its sides

Then, the perimeter of the room is AB + BC + CD + DE + EF + FG + GH + HA

Therefore, the perimeter of the room is 2 + 2 + 3 + 2 + 2 + 6 + 7 + 6 = 30 m

ii. Then area of rectangle AHGF = 6 × 7 = 42 m²

And the area of rectangle BCDE = 3 × 2 = 6 m²

Then, the area of the floor = Area of rectangle AHGF – Area of rectangle BCDE

Therefore, the area of the floor = 42 – 6 = 36 m²

iii. The area of a rectangle is (Length)(Breadth)

Then area of rectangle AHGF =  6 × 7 = 42 m³

And the area of rectangle BCDE = 3 × 2 = 6 m³

Then, the area of the floor = Area of rectangle AHGF – Area of rectangle BCDE

The area of the floor = 42 – 6 = 36 m³

Now the volume of the room = (Area of the floor) × (Height)

Therefore, the volume of the room is 36 × 3 = 108 m³