Question

27 Sakura has a birdhouse with rectangular walls, a rectangular bottom, and a rectangular entry.like the one modeled below.4 in.10 inT5 in.6 in.4010 in.She will paint the four outside walls but not the bottom or the roof of the birdhouse. What isthe area that Sakura will paint?A 320 in.B 160 in.?C 300 in.D 140 in.s.ph

Answer 1

We want to find the total area that Sakura will paint. Based on the given figure, the side walls have the dimension of 10 in by 6 in while the front and back walls have the dimension of 10 in by 10 in. Basically, we want to sum up the total area of these 4 walls to get the total area that Sakura will paint.

The side walls represent a rectangle. The area of the rectangle can be computed via the equation

`A_(rec\tan gle)=lxw`

Hence, the area of one side wall is equal to

`A_(sidewall)=10*6=60in^2`

For two side walls, we just multiply the area of one sidewall by 2, having

`2* A_(sidewall)=120in^2`

We are left with the back wall and front wall of the birdhouse. We can say that they have the same dimension but the front wall has a hole that will not be painted. The dimensions of the front and back wall are 10 in x 10 in. Hence, for the back wall, which doesn't have any opening, the total area would be

`A_(backwall)=10*10=100in^2`

For the front wall, you have an opening with a dimension of 4 in by 5 in. The area of the opening, or the door, is

`A_(door)=4*5=20in^2`

The total area for the front wall would be the area of the back wall minus the area of the door of the birdhouse. Hence, we have

`A_(frontwall)=100in^2-20in^2=80in^2`

The total area that Sakura paint is just the sum of the areas of the four outside walls, which is just represented in mathematical expression as

`A_(tot)=2A_(sidewall)+A_(backwall)+A_(frontwall)_{}`

Substitute the computed area of the walls on the expression above and compute, we get

`A_(tot)=120in^2+80in^2+100in^2=300in^2`

Therefore, the answer is the letter C.