Find the area of the figure. Hint: Separate into regular shapes and combine the areas!

Shapes: 1 rectangle and 2 triangles
Rectangle: 11 m and 3 m
Triangle 1: 7 m and 4 m
Triangle 2: 7 m and 4 m
A = [ ? ] m²
Area Formulas: B x H and B x H/2

1 answer

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: \[ \boxed{61} , \text{m}^2 \]