Problem Breakdown

The task is to calculate the shaded area. The diagram consists of:

1. A larger rectangle with dimensions $15 \, \text{m} \times 9 \, \text{m}$.
2. A smaller rectangle inside the larger rectangle, oriented diagonally.

The shaded area is the area of the larger rectangle minus the area of the smaller (diagonal) rectangle.

Step-by-Step Solution

1. Calculate the area of the larger rectangle

The area of the larger rectangle is: $\text{Area} = \text{Length} \times \text{Width}$ $\text{Area} = 15 \, \text{m} \times 9 \, \text{m} = 135 \, \text{m}^2$

2. Determine the area of the smaller rectangle

To calculate the area of the smaller rectangle, we need its diagonal dimensions.

The smaller rectangle has:

• One side $5 \, \text{m}$,
• One side $3 \, \text{m}$.

Its area is: $\text{Area} = \text{Length} \times \text{Width}$ $\text{Area} = 5 \, \text{m} \times 3 \, \text{m} = 15 \, \text{m}^2$

3. Calculate the shaded area

The shaded area is the area of the larger rectangle minus the area of the smaller rectangle: $\text{Shaded Area} = \text{Area of Larger Rectangle} - \text{Area of Smaller Rectangle}$ $\text{Shaded Area} = 135 \, \text{m}^2 - 15 \, \text{m}^2 = 120 \, \text{m}^2$

Final Answer:

The shaded area is: $\boxed{120 \, \text{m}^2}$

Do you want further clarification, or should I explain any step in more detail? Let me know!

Related Questions:

1. How would the solution change if the smaller rectangle's orientation was not diagonal?
2. What happens to the shaded area if the dimensions of the larger rectangle are doubled?
3. How can you calculate the smaller rectangle's area using its diagonal and trigonometry?
4. What would the shaded area be if the smaller rectangle was a square?
5. Can the shaded area ever exceed the area of the smaller rectangle?

Tip:

Always double-check whether diagonal shapes are correctly calculated; using trigonometry might be necessary for tilted rectangles!