To find the area of the figure, we can separately calculate the areas of the rectangle and the two triangles, and then combine those areas.
Step 1: Calculate the area of the rectangle
The area \( A \) of a rectangle is calculated using the formula:
\[ A = \text{Base} \times \text{Height} \]
For the rectangle, using the given dimensions:
\[ \text{Base} = 16 , \text{ft}, \quad \text{Height} = 4 , \text{ft} \]
So, the area of the rectangle is:
\[ A_{\text{rectangle}} = 16 , \text{ft} \times 4 , \text{ft} = 64 , \text{ft}^2 \]
Step 2: Calculate the area of the first triangle
The area \( A \) of a triangle is calculated using the formula:
\[ A = \frac{\text{Base} \times \text{Height}}{2} \]
For Triangle 1, both the base and height are 8 ft:
\[ A_{\text{triangle 1}} = \frac{8 , \text{ft} \times 8 , \text{ft}}{2} = \frac{64 , \text{ft}^2}{2} = 32 , \text{ft}^2 \]
Step 3: Calculate the area of the second triangle
For Triangle 2, we will use the same formula as above, since it has the same dimensions:
\[ A_{\text{triangle 2}} = \frac{8 , \text{ft} \times 8 , \text{ft}}{2} = \frac{64 , \text{ft}^2}{2} = 32 , \text{ft}^2 \]
Step 4: Combine the areas
Now, we can combine the areas of the rectangle and the two triangles:
\[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle 1}} + A_{\text{triangle 2}} \] \[ A_{\text{total}} = 64 , \text{ft}^2 + 32 , \text{ft}^2 + 32 , \text{ft}^2 = 128 , \text{ft}^2 \]
Final Answer
The total area of the figure is:
\[ A = 128 , \text{ft}^2 \]
So, the answer is:
\[ A = 128 , \text{ft}^2 \]