Question

Suppose a rectangular room with a length of 6m width of 4m and height of 3m is to be renovated for the forthcoming holiday, if the roof and all the interior walls with the exception of a door with 2m length and 0.8 width are to be renovated. What is the total area for the renovation

Answer 1

$\LARGE{ \underline{\underline{ \sf{Required \: answer:}}}}$

GiveN:

• Dimensions of the room = 6 m × 4 m × 3 m
• It was to be renovated except the door and the floor.
• Dimension of the door = 2 m × 0.8 m

To FinD:

• Total area of renovation?

Step-wise-Step Explanation:

The total area to be renovated will be the total surface area of the room - (the area of the floor + area of door). Total surface area of the room:

$\large{\cdot{\underline{\boxed{ \rm{TSA = 2(lb + bh + hl)}}}}}$

And area of the floor will be lb. Plugging the given values in the equation we derived.

• Total renovation area = 2(lb + bh + hl) - lb - length of door × width of the door.

= 2(6×4 + 4×3 + 3×6) - 6×4 - 2×0.8 m²

= 2(24 + 12 + 18) - 24 - 1.6 m²

= 2(54) - 24 - 1.6 m²

= 108 - 24 - 1.6 m²

= 82.4 m²

The total area to be renovated is 82.4 m².

And we are done! :D

Answer 2

Answer:

Given:-

• Dimensions of door = 2m × 0.8m
• Dimensions of rectangular room = 6m×4m×3m
• It was renovated expect door and floor

Find:-

• What is the total area for the renovation??

Solution:-

From the question...

Renovated area = TSA of room - area of floor + area of door

TSA of room :-

We know that ⤵

${ \boxed{ \sf{TSA \: of \: rectangle = 2(lb + bh + hl)}}}$

${ \to{2(6 \times 4 + 4 \times 3 + 3 \times 6)}}$

${ \to{2(24 + 12 + 18)}}$

${ \to{2(54)}}$

${ \to{108}}$

So, TSA of room is 108m²

Area of floor:-

${ \boxed{ \sf{area = length \times breadth}}}$

${ \to{Area = 6 \times 4}}$

${ \to{{Area = 24}}}$

So, the area of floor is 24m²

Area of door :-

${ \boxed{ \sf{Area \: of \: door =length \times width }}}$

${ \to{Area = 2 \times 0.8}}$

${ \to{Area = 1.6 }}$

So, the area of door is 1.6m²

Renovated area:-

Renovated area = TSA of room - area of floor + area of door

${ \to{108 - 24 + 1.6}}$

${ \to{84 + 1.6}}$

${ \to{85.6 }}$

↪Therefore, the total area of renovation is 85.6m²