. Allie is helping her parents paint the four exterior walls of the backyard shed. The length from the front to

the back of the shed is 10 ft, the width across the front and back is 8 ft, and the height is 6 ft. The door
opening on the front of the shed has a width of 55 1
2 in. and a height of 60 in.
(a) What is the surface area to be painted? Show your work.
(b) The paint costs $12.97 per quart and each quart covers 105 ft2
. Allie’s parents want to apply a primer coat
to the walls before they apply the paint. The primer will help the paint go on more smoothly and last
longer. One quart of primer costs $6.98 and also covers 105 ft2
. How much will it cost to paint the shed if
Allie’s family applies one coat of primer and one coat of paint? Show your work.

(a) 376ft2

70$

To find the surface area to be painted, we need to find the area of each individual wall and then sum them up.

(a) Let's start by finding the areas of each wall:

Wall 1: The front and back wall, which has a height of 6 ft and a width of 8 ft. Therefore, the area is 6 ft * 8 ft = 48 ft^2.

Wall 2: The left and right walls, which have a height of 6 ft and a length of 10 ft. Therefore, the area is 6 ft * 10 ft = 60 ft^2.

Wall 3: The top of the shed. It has a length of 10 ft and a width of 8 ft, so the area is 10 ft * 8 ft = 80 ft^2.

Now, we need to subtract the area of the door opening in the front wall:

Door area = width * height = 55 1/2 in * 60 in.

Since the dimensions are in different units, we need to convert them to the same unit. Let's convert the width to inches:

55 1/2 in = 55 in + 1/2 in = 55 in + 0.5 in = 55.5 in.

Now, the door area = 55.5 in * 60 in = 3330 in^2.

Now, let's convert the door area to square feet:

3330 in^2 * (1 ft/12 in)^2 = 18.375 ft^2.

Finally, we can calculate the total surface area to be painted by summing up the areas of the walls:

Total surface area = 2 * (Wall 1 + Wall 2) + Wall 3 - Door area
Total surface area = 2 * (48 ft^2 + 60 ft^2) + 80 ft^2 - 18.375 ft^2

Simplifying the equation, we get:

Total surface area = 216.625 ft^2.

So, the surface area to be painted is 216.625 ft^2.

(b) To calculate the cost of painting the shed, we'll need to know the total surface area to be painted and the cost per quart of primer and paint.

We already found the total surface area to be painted, which is 216.625 ft^2.

Now, let's calculate the number of quarts of primer needed:

Number of quarts of primer needed = Total surface area / Coverage per quart
Number of quarts of primer needed = 216.625 ft^2 / 105 ft^2 = 2.063 quarts.

Since we can't have a fraction of a quart, we will round up to the nearest whole number. Therefore, we'll need 3 quarts of primer.

Now, let's calculate the cost of primer:

Cost of primer = Number of quarts of primer needed * Cost per quart
Cost of primer = 3 quarts * $6.98/quart = $20.94.

Next, let's calculate the number of quarts of paint needed:

Number of quarts of paint needed = Total surface area / Coverage per quart
Number of quarts of paint needed = 216.625 ft^2 / 105 ft^2 = 2.063 quarts.

Again, we round up to the nearest whole number. We'll need 3 quarts of paint.

Now, let's calculate the cost of paint:

Cost of paint = Number of quarts of paint needed * Cost per quart
Cost of paint = 3 quarts * $12.97/quart = $38.91.

Finally, we can find the total cost of painting the shed by adding the cost of primer and paint:

Total cost of painting = Cost of primer + Cost of paint
Total cost of painting = $20.94 + $38.91 = $59.85.

So, it will cost $59.85 to paint the shed if one coat of primer and one coat of paint are applied.