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

1 answer

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:

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