To find the area of the figure, we will calculate the area of the rectangle and the two triangles separately, then combine those areas.
Step 1: Area of the Rectangle
The area \( A \) of a rectangle is given by the formula: \[ A = \text{Base} \times \text{Height} \] For the rectangle:
- Base = 11 m
- Height = 3 m
Calculating the area: \[ A_{\text{rectangle}} = 11 , \text{m} \times 3 , \text{m} = 33 , \text{m}^2 \]
Step 2: Area of Triangle 1
The area \( A \) of a triangle is given by the formula: \[ A = \frac{\text{Base} \times \text{Height}}{2} \] For Triangle 1:
- Base = 7 m
- Height = 4 m
Calculating the area: \[ A_{\text{triangle 1}} = \frac{7 , \text{m} \times 4 , \text{m}}{2} = \frac{28 , \text{m}^2}{2} = 14 , \text{m}^2 \]
Step 3: Area of Triangle 2
For Triangle 2, the base and height are the same as Triangle 1:
- Base = 7 m
- Height = 4 m
Calculating the area: \[ A_{\text{triangle 2}} = \frac{7 , \text{m} \times 4 , \text{m}}{2} = \frac{28 , \text{m}^2}{2} = 14 , \text{m}^2 \]
Step 4: Combine the Areas
Now, we combine the areas of the rectangle and the two triangles: \[ \text{Total Area} = A_{\text{rectangle}} + A_{\text{triangle 1}} + A_{\text{triangle 2}} \] \[ \text{Total Area} = 33 , \text{m}^2 + 14 , \text{m}^2 + 14 , \text{m}^2 \] \[ \text{Total Area} = 33 , \text{m}^2 + 28 , \text{m}^2 = 61 , \text{m}^2 \]
Final Answer
The total area of the figure is: \[ \boxed{61} , \text{m}^2 \]