Let's go through each question and check the answers provided to ensure they are correct. I will analyze each question based on the visual information provided and attempt to solve them.

Problem Analysis

Question 9

• 9(a) asks for the area of parallelogram $A$.

  • Given: The area of parallelogram $A$ is $75 \, \text{cm}^2$.
  • The answer provided is 75 cm², which seems correct based on the information given.

• 9(b) asks for the area of the whole figure.

  • This includes both the parallelogram $A$ and the trapezium $B$.
  • To solve, we would need the area of trapezium $B$ (not provided explicitly here).
  • The student’s answer is scratched out, and there’s a correction attempted at 450 cm², but without more information, it’s unclear if this is correct.

Question 10

• 10 involves three identical trapeziums, and it’s asking for the area of each trapezium.
  • The area of each trapezium is also scratched out, and without further dimensions or area provided, it's challenging to verify if this is correct.

Question 11

• 11 asks for the area of the trapezium among three squares.
  • Given answer choices (A) 8 m², (B) 16 m², (C) 28 m², and (D) 56 m².
  • Based on the layout of squares with known areas, it looks like (B) 16 m² might be correct, which aligns with the selected answer.

Question 12

• 12 deals with a quadrilateral divided into a triangle $C$ and a trapezium $D$.
  • Given: The area of trapezium $D$ is $300 \, \text{cm}^2$.
  • Additional steps would be required to verify if calculations or follow-up answers on this part are correct.

Summary

Based on the visual details provided, it looks like the student’s answers might be mostly correct, but we’d need additional measurements or explicit area values to verify for 9(b) and 10 especially.

Would you like a detailed breakdown on solving each of these problems or further clarification on any specific question?

Follow-Up Questions

1. How do we calculate the area of a trapezium given its dimensions?
2. What is the formula to find the area of a parallelogram?
3. What approach can we use if only partial dimensions of a shape are provided?
4. How can we determine the total area of a composite figure?
5. How to verify answers in a multi-step geometric problem like these?

Tip:

When working on area problems with composite shapes, break down each shape individually, calculate areas, and then sum them up for total area verification.