Let's solve the problem step by step:

Given:

• Rectangle dimensions: Length = 10 cm, Height = 7 cm
• Triangle dimensions: Base = 10 cm, Height = 5 cm

Solution:

(a) Area of the Rectangle:

The formula for the area of a rectangle is:

$\text{Area} = \text{Length} \times \text{Height}$

Substitute the given values:

$\text{Area of Rectangle} = 10 \times 7 = 70 \, \text{cm}^2$

(b) Area of the Triangle:

The formula for the area of a triangle is:

$\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$

Substitute the given values:

$\text{Area of Triangle} = \frac{1}{2} \times 10 \times 5 = 25 \, \text{cm}^2$

(c) Total Area of the Whole Shape:

The whole shape consists of the rectangle and the triangle, so:

$\text{Total Area} = \text{Area of Rectangle} + \text{Area of Triangle}$

Substitute the calculated values:

$\text{Total Area} = 70 + 25 = 95 \, \text{cm}^2$

Final Answer:

• (a) Area of the Rectangle = 70 cm²
• (b) Area of the Triangle = 25 cm²
• (c) Total Area of the Whole Shape = 95 cm²

Would you like further clarification or additional examples?

Follow-Up Questions:

1. How would the total area change if the rectangle’s height increased to 8 cm?
2. What is the perimeter of the whole shape?
3. Can you calculate the percentage of the total area that is made up by the triangle?
4. What happens to the area if both dimensions of the rectangle are doubled?
5. How would you calculate the area if the triangle's height changed?

Tip:

Always double-check your units (e.g., cm, m) to ensure the measurements are consistent when calculating areas or other geometric properties.