To solve the problem, we need to calculate the total area of the trapezium (orange) and the parallelogram (blue). Here's how we proceed:

Step 1: Area of the trapezium

The formula for the area of a trapezium is: $\text{Area} = \frac{1}{2} \times (\text{a} + \text{b}) \times h$ Where:

• $a$ = top length = 23 cm
• $b$ = bottom length = 14 cm
• $h$ = height = 13 cm

Substitute the values: $\text{Area of trapezium} = \frac{1}{2} \times (23 + 14) \times 13 = \frac{1}{2} \times 37 \times 13 = 240.5 \, \text{cm}^2$

Step 2: Area of the parallelogram

The formula for the area of a parallelogram is: $\text{Area} = \text{base} \times \text{height}$ Where:

• Base = 14 cm
• Height = 5 cm

Substitute the values: $\text{Area of parallelogram} = 14 \times 5 = 70 \, \text{cm}^2$

Step 3: Total area

$\text{Total area} = \text{Area of trapezium} + \text{Area of parallelogram} = 240.5 + 70 = 310.5 \, \text{cm}^2$

Final Answer:

The total area is: $\boxed{310.5 \, \text{cm}^2}$

Would you like a breakdown of any particular step or further clarifications? 😊

Related Questions:

1. How would the formula for the area change if the trapezium had slanted sides instead of a vertical height?
2. Can the formula for a parallelogram be derived geometrically? If so, how?
3. What would happen to the area calculations if the dimensions were doubled?
4. How do the formulas for trapezium and parallelogram compare to that of a triangle?
5. What are real-life applications where calculating the areas of these shapes is necessary?

Tip:

Always double-check whether dimensions like height refer to vertical distance or slanted lengths, as this can change the calculation approach!