The given shape consists of a rectangle and a right triangle. To calculate the area of the whole shape, we need to find the areas of both the rectangle and the triangle and then add them together.

Step 1: Calculate the area of the rectangle

The dimensions of the rectangle are:

• Length = $10 \, \text{cm}$
• Width = $7 \, \text{cm}$

The area of a rectangle is given by: $\text{Area of rectangle} = \text{Length} \times \text{Width}$

Substitute the values: $\text{Area of rectangle} = 10 \times 7 = 70 \, \text{cm}^2$

Step 2: Calculate the area of the triangle

The triangle is a right triangle with:

• Base = $4 \, \text{cm}$
• Height = $5 \, \text{cm}$

The area of a triangle is given by: $\text{Area of triangle} = \frac{1}{2} \times \text{Base} \times \text{Height}$

Substitute the values: $\text{Area of triangle} = \frac{1}{2} \times 4 \times 5 = 2 \times 5 = 10 \, \text{cm}^2$

Step 3: Add the areas of the rectangle and triangle

$\text{Total Area} = \text{Area of rectangle} + \text{Area of triangle}$ $\text{Total Area} = 70 + 10 = 80 \, \text{cm}^2$

Final Answer:

The total area of the whole shape is: $\boxed{80 \, \text{cm}^2}$

Do you want more detailed explanations, or do you have any questions?

Relative Questions:

1. How do we find the area of other polygons like trapeziums?
2. Can the shape be divided differently to simplify calculations?
3. What would happen if the height of the triangle were different but the base remained the same?
4. How can this problem be solved using coordinate geometry?
5. What formulas are essential to solving composite shape problems efficiently?

Tip:

Always identify individual components of a composite shape to break down the problem systematically!