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Wendell is designing the layout of the backyard behind his new home. He wants to build a dog house and add some flower gardens. In the following tasks, you will help Wendell create a scale drawing of his backyard to help him plan the location and size of the dog house and gardens. The provided sketch is not drawn to scale, but it does give the actual dimensions of the lawn in feet. The backyard is a trapezoid—the west side is perpendicular to both the north and south sides, and the deck is a rectangle.

Wendell’s backyard is a trapezoid where the west side is perpendicular to both the north and south sides, and the deck is a rectangle.


Part A                                                                                                                                                                      
If Wendell creates a scale drawing using the scale 1 inch to 10 feet, what will the dimensions of the deck in the scale drawing be?




Part B
In the scale drawing, what will the length of the east side of the backyard be?




Part C
In the scale drawing, what will the length of the south side of the backyard be?





Part D
In the scale drawing, what will the length of the west side of the backyard be?



Part E
In the scale drawing, what will the length of the north side of the backyard be?




Part F
Two corners of the backyard are right angles. The third corner forms an obtuse angle measuring 127º. The fourth corner forms an acute angle measuring 53º. When transferring these angle measurements from the real world to the scale drawing, will their measures increase, decrease, or stay the same?



Part G
In the scale drawing, what is the area of the lawn (that is, the area of the whole backyard, except for the deck)?

Let's address each part of the problem systematically.

### Part A
**Dimensions of the deck in the scale drawing:**
The deck dimensions are given as 10 feet by 8 feet. Using the scale 1 inch to 10 feet, the dimensions in the scale drawing will be:
- Length: \( \frac{10 \text{ feet}}{10} = 1 \text{ inch} \)
- Width: \( \frac{8 \text{ feet}}{10} = 0.8 \text{ inches} \)

### Part B
**Length of the east side of the backyard in the scale drawing:**
The east side of the backyard is given as 35 feet. Using the scale 1 inch to 10 feet, the length in the scale drawing will be:
\[ \frac{35 \text{ feet}}{10} = 3.5 \text{ inches} \]

### Part C
**Length of the south side of the backyard in the scale drawing:**
The south side of the backyard is given as 71 feet. Using the scale 1 inch to 10 feet, the length in the scale drawing will be:
\[ \frac{71 \text{ feet}}{10} = 7.1 \text{ inches} \]

### Part D
**Length of the west side of the backyard in the scale drawing:**
The west side of the backyard is given as 28 feet. Using the scale 1 inch to 10 feet, the length in the scale drawing will be:
\[ \frac{28 \text{ feet}}{10} = 2.8 \text{ inches} \]

### Part E
**Length of the north side of the backyard in the scale drawing:**
The north side of the backyard is given as 50 feet. Using the scale 1 inch to 10 feet, the length in the scale drawing will be:
\[ \frac{50 \text{ feet}}{10} = 5 \text{ inches} \]

### Part F
**Transfer of angle measurements to the scale drawing:**
The angle measurements will stay the same when transferred to the scale drawing. Angles are dimensionless and do not change with scaling.

### Part G
**Area of the lawn in the scale drawing:**
The area of the trapezoid (the lawn) minus the area of the deck needs to be calculated.

First, calculate the area of the entire backyard (trapezoid):
\[ \text{Area of trapezoid} = \frac{1}{2} \times (b_1 + b_2) \times h \]
where \( b_1 = 71 \) feet (south side), \( b_2 = 50 \) feet (north side), and \( h = 28 \) feet (west side, the height of the trapezoid).

\[ \text{Area of trapezoid} = \frac{1}{2} \times (71 + 50) \times 28 \]
\[ \text{Area of trapezoid} = \frac{1}{2} \times 121 \times 28 \]
\[ \text{Area of trapezoid} = \frac{1}{2} \times 3388 \]
\[ \text{Area of trapezoid} = 1694 \text{ square feet} \]

Then, calculate the area of the deck:
\[ \text{Area of deck} = 10 \times 8 = 80 \text{ square feet} \]

Subtract the area of the deck from the area of the trapezoid to get the area of the lawn:
\[ \text{Area of lawn} = 1694 - 80 = 1614 \text{ square feet} \]

To represent this in the scale drawing:
\[ \text{Area in scale drawing} = \frac{1614}{(10^2)} = 16.14 \text{ square inches} \]

Would you like any more details or have any questions about these calculations? 

Here are 5 numbered questions you might want to ask:
1. How do you calculate the area of a trapezoid?
2. How can I convert feet to inches using a scale drawing?
3. What is the significance of keeping angles the same in scale drawings?
4. How do you determine the dimensions of an object in a scale drawing?
5. How can you verify the calculations for area in different units?

**Tip:** When working with scale drawings, always ensure your units are consistent to avoid errors in your calculations.

Explore how to create a scale drawing for Wendell's backyard, including determining the dimensions of the deck and various sides of the backyard in the scale drawing. Calculate the area of the lawn, considering the scale factor and geometric formulas. Suitable for students in Grades 6-8.

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