Find the area of the figure.

Hint: Separate into regular shapes and combine the areas!
Shapes: Rectangle and a triangle
Triangle: 6 in
Rectangle: 6 in and 11 in
A = [ ? ] in²
Area Formulas: B x H and B x H/2

1 answer

To find the area of the figure by separating it into a rectangle and a triangle, we can use the following area formulas.

Step 1: Calculate the 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 (B) = 11 in
  • Height (H) = 6 in

So, the area of the rectangle is:

\[ A_{rectangle} = 11 , \text{in} \times 6 , \text{in} = 66 , \text{in}^2 \]

Step 2: Calculate the area of the triangle

The area \( A \) of a triangle is given by the formula:

\[ A = \frac{1}{2} \times \text{Base} \times \text{Height} \]

For the triangle:

  • Base (B) = 6 in (assuming this is the base of the triangle you mentioned)
  • Height (H) = 6 in

So, the area of the triangle is:

\[ A_{triangle} = \frac{1}{2} \times 6 , \text{in} \times 6 , \text{in} = \frac{1}{2} \times 36 , \text{in}^2 = 18 , \text{in}^2 \]

Step 3: Combine the areas

Now, add the areas of the rectangle and the triangle:

\[ \text{Total Area} = A_{rectangle} + A_{triangle} = 66 , \text{in}^2 + 18 , \text{in}^2 = 84 , \text{in}^2 \]

So, the total area of the figure is:

\[ \boxed{84} , \text{in}^2 \]