Question

Find the area of the figure. Hint: Separate into regular shapes and combine the areas!
Shapes: 1 rectangle and 2 triangles
Triangle 1: 8 ft and 8 ft
Triangle 2: 8 ft and 8 ft
Rectangle: 16 ft and 4 ft
A = [ ? ] in²
Area Formulas: B x H and B x H/2

Answer 1

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:

\[
A = 128 \, \text{ft}^2
\]