)a room measures 15 feet long and 12 feet wide, with a 9-foot ceiling. there is a single doorway in one wall that measures 3 feet × 7 feet that does not get painted. what is the area of the walls that requires paint?

825 feet of area of the wall  required to be  painted.

Explanation:

Given:

Length of the room = 15 feet

Width of the room =12 feet

Height of the room = 9-foot

Size of the door= 3 feet x 7 feet

To find:

The area of the walls that requirespainted=?

Solution:

We know that,  

Area of walls that need paint = total surface area of room – area of door that doesn’t need paint…………(1)

Finding the Total area of the room:

room is cuboidal shape,  

Then, its total surface area = 2(lb + bh + hl)

Where

h is height,  

l is length,

b is width  

Substituting the values,

Total surface area = 2(15 x 12 + 12 5 9 + 9 x 15)  

Total surface area = 2(180+108+135)

Total surface area = 2( 423)

Total surface area =  = 846 feet…………..(2)  

Finding the area of the door:

Area of door = area of rectangle = length x width

Substituting the values,

area of door= 3 x 7 = 21 feet……………(3)

Substituting (2) and (3) in (1)

Area that  is require paint = 846 – 21 = 825 feet

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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