To find the area of the lawn, we need to calculate the area of the whole backyard and then subtract the area of the deck.

The shape of the backyard appears to be a trapezoid, and we can use the formula for the area of a trapezoid: $A_{\text{trapezoid}} = \frac{1}{2} \times (b_1 + b_2) \times h$ where $b_1$ and $b_2$ are the lengths of the parallel sides and $h$ is the height (the perpendicular distance between the parallel sides).

From the diagram:

• $b_1 = 50$ units
• $b_2 = 71$ units
• $h = 28$ units

Thus, the area of the trapezoid is: $A_{\text{trapezoid}} = \frac{1}{2} \times (50 + 71) \times 28$ $A_{\text{trapezoid}} = \frac{1}{2} \times 121 \times 28$ $A_{\text{trapezoid}} = 60.5 \times 28$ $A_{\text{trapezoid}} = 1694 \text{ square units}$

Next, we need to find the area of the deck. The deck is a rectangle with dimensions:

• $10$ units by $8$ units

The area of the deck is: $A_{\text{deck}} = 10 \times 8 = 80 \text{ square units}$

Finally, the area of the lawn is the area of the whole backyard minus the area of the deck: $A_{\text{lawn}} = 1694 - 80 = 1614 \text{ square units}$

So, the area of the lawn is $1614$ square units.

Would you like more details or have any questions?

Here are some more questions you might want to ask:

1. How do you calculate the area of a different shape?
2. What is the perimeter of the lawn?
3. How can you verify the measurements in a scale drawing?
4. How do you find the dimensions of a shape if you only know its area?
5. Can you explain how to calculate the area of irregular polygons?

Tip: When working with scale drawings, always verify the dimensions and ensure you understand the units of measurement being used.