Question

karen is planning to texture - coat a building whose dimensions are shown below. the front of the building has a window measuring 39 in by 4 ft and a door measuring 3 ft by 80 in. the left and right sides of the building each have a window measuring 16 ft by 4 ft. the back of the building has no window or door. use the given information to answer the questions. each tab shows a different view of the building.
(a) assuming the roof, windows, and door require no texture - coat, what is the area in square feet that needs texture - coat? (do not round any intermediate computations and give your answer as a whole number.)
(square) (ft^{2})
(b) karen will use texture - coat that is sold in cans. each can contains enough texture - coat to cover (270) (ft^{2}). assume karen doesnt have any texture - coat yet and she cant buy partial cans. how many cans will she need to buy in order to texture - coat the building?
(square) cans
(c) if each can costs $11.50, how much will karen need to spend on texture - coat?
(square) $

Explanation:

Part (a)

Step 1: Convert all dimensions to feet

First, convert the window dimensions from inches to feet. The left and right windows: \( 80 \) inches \( = \frac{80}{12}=\frac{20}{3}\approx6.67 \) ft. So each left/right window is \( 3 \) ft \( \times\frac{20}{3}\) ft \( = 20 \) ft². The front window: \( 39 \) inches \(=\frac{39}{12}=\frac{13}{4} = 3.25 \) ft, so front window area is \( 3.25 \) ft \( \times4 \) ft \( = 13 \) ft². The other window (back - left? Wait, the problem says front has a window (39 in by 4 ft), left and right each have a window (3 ft by 80 in), back has no window/door. Now, calculate the surface area of the building. Let's assume the building has front, back, left, right, and maybe the sides? Wait, the diagram shows front - right view with height 14 ft, length 28 ft, and a 10 ft dimension. Wait, maybe the building is a rectangular prism - like structure. Let's re - read: The front of the building: let's find the area of each face.

Front face: height 14 ft, length 28 ft? Wait, no, the front has a window (39 in = 3.25 ft by 4 ft). So front area: \( 14\times28 - 3.25\times4\). Back face: \( 14\times28\) (no window/door). Left and right faces: each has a window (3 ft by 80 in = 3 ft by \( \frac{20}{3}\) ft = 20 ft²). The left and right faces: let's see, the height of the building is 14 ft, and the width? Wait, maybe the building has length \( L = 28 \) ft, width \( W = 10 \) ft, height \( H = 14 \) ft. Wait, the front - right view: 14 ft (height), 28 ft (length), 10 ft (depth). So the surface area to be textured (excluding roof? Wait, the problem says "assuming the roof, windows, and door require no texture - coat" – wait, no, "needs texture - coat, what is the area in square feet that needs texture - coat? (Do not round any intermediate computations and give your answer as a whole number.)" Wait, maybe I misread. Wait, the building's exterior walls: front, back, left, right.

Front wall: area \( A_{front}=14\times28 - 3.25\times4\) (subtract front window). Back wall: \( A_{back}=14\times28\) (no window/door). Left wall: \( A_{left}=14\times10 - 20\) (subtract left window, 3 ft×80 in = 20 ft²). Right wall: \( A_{right}=14\times10 - 20\) (subtract right window).

Calculate each:

\( A_{front}=14\times28 - 3.25\times4=392 - 13 = 379 \)

\( A_{back}=14\times28 = 392 \)

\( A_{left}=14\times10 - 20=140 - 20 = 120 \)

\( A_{right}=14\times10 - 20 = 120 \)

Total area \( A = 379+392 + 120+120\)

\( 379+392=771\), \( 120 + 120 = 240\), \( 771+240 = 1011\) Wait, that can't be right. Wait, maybe the windows: the left and right windows are 3 ft by 80 in. 80 in is \( \frac{80}{12}=\frac{20}{3}\) ft, so area of each left/right window is \( 3\times\frac{20}{3}=20 \) ft². The front window: 39 in is \( \frac{39}{12}=\frac{13}{4}=3.25 \) ft, so area is \( 3.25\times4 = 13 \) ft².

Now, let's consider the building's walls:

• Front wall: Let's assume the height of the wall is 14 ft and the length is 28 ft. So front wall area (without window): \( 14\times28=392 \) ft². Subtract front window: \( 392 - 13 = 379 \) ft².
• Back wall: \( 14\times28 = 392 \) ft² (no window/door).
• Left wall: Let's assume the height is 14 ft and the width is 10 ft. Area without window: \( 14\times10 = 140 \) ft². Subtract left window: \( 140 - 20 = 120 \) ft².
• Right wall: Same as left wall: \( 14\times10 - 20 = 120 \) ft².

Now, sum all these areas: \( 379+392 + 120+120=1011 \) ft². Wait, but maybe we missed the roof? No, the problem says "assuming the roof, windows, and door require no texture - coat", so we don't include the roof. Wait, maybe the building h…

Step 1: Divide total area by coverage per can

Each can covers \( 270\) ft². We have a total area of \( 1011\) ft². So the number of cans \( n=\frac{1011}{270}\approx3.74\). Since she can't buy partial cans, we round up to the next whole number.

Step 2: Round up the result

\( \lceil\frac{1011}{270}
ceil=\lceil3.74
ceil = 4\)

Step 1: Multiply number of cans by cost per can

Each can costs \( \$11.50\) and she needs 4 cans. So total cost \( C = 4\times11.50\)

Step 2: Calculate the product

\( 4\times11.50=\$46.00\)

Answer:

(part a): \( 1011\) ft²

Part (b)