To find the total area ($A_T$) of the shape in the image, we need to calculate the area of two parts: a rectangle and a triangle above it.

1. Area of the Rectangle

The rectangle has a width of $4 \, \text{cm}$ and a height of $9 \, \text{cm}$.

$\text{Area of Rectangle} = \text{Width} \times \text{Height} = 4 \, \text{cm} \times 9 \, \text{cm} = 36 \, \text{cm}^2$

2. Area of the Triangle

The triangle above the rectangle has a base of $4 \, \text{cm}$ (same as the width of the rectangle) and a height of $3.5 \, \text{cm}$.

$\text{Area of Triangle} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 4 \, \text{cm} \times 3.5 \, \text{cm} = 7 \, \text{cm}^2$

3. Total Area of the Shape

To find the total area, we sum the areas of the rectangle and the triangle:

$A_T = 36 \, \text{cm}^2 + 7 \, \text{cm}^2 = 43 \, \text{cm}^2$

Final Answer

$A_T = 43 \, \text{cm}^2$

Would you like further details or have any questions?

Here are some related questions you might find helpful:

1. How do you find the area of composite shapes?
2. What is the formula for the area of a triangle?
3. How do different types of triangles affect area calculation?
4. How can we determine the perimeter of the given shape?
5. What other methods could be used to find the total area?

Tip: When working with composite shapes, always identify and separate them into simpler shapes like rectangles and triangles for easier area calculation.