The figure consists of a rectangle at the bottom and a triangle on top of it.

Step 1: Area of the rectangle

The dimensions of the rectangle are:

• Height = 4 cm
• Base = 6 cm

The formula for the area of a rectangle is: $\text{Area of rectangle} = \text{base} \times \text{height}$ $\text{Area of rectangle} = 6 \, \text{cm} \times 4 \, \text{cm} = 24 \, \text{cm}^2$

Step 2: Area of the triangle

The triangle has:

• Base = 6 cm (same as the width of the rectangle)
• Height = 5 cm (given in the image)

The formula for the area of a triangle is: $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$ $\text{Area of triangle} = \frac{1}{2} \times 6 \, \text{cm} \times 5 \, \text{cm} = 15 \, \text{cm}^2$

Step 3: Total area of the figure

The total area is the sum of the area of the rectangle and the area of the triangle: $\text{Total area} = 24 \, \text{cm}^2 + 15 \, \text{cm}^2 = 39 \, \text{cm}^2$

Final Answer:

The total area of the figure is 39 cm².

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you find the perimeter of this composite shape?
2. How would the total area change if the height of the triangle doubled?
3. How is the area of a triangle different from that of a rectangle in terms of formulas?
4. What happens to the area if both dimensions of the rectangle are doubled?
5. Can you calculate the area of the figure if it had a different shape, like a semicircle on top?

Tip: Always check if shapes in a diagram are composite (combination of simpler shapes) to break down calculations step-by-step.