Hey everyone! In this quick, CSSE Area and Perimeter video, we’ll be taking a look at a question from the 2015 CSSE paper to help out one of our students. We thought it would be great to share this on YouTube so that everyone can benefit from the explanation. The question we’ll be focusing on involves a grid with various shapes, each labelled with a letter. Let’s dive in and see what we can learn!
Understanding this CSSE Area and Perimeter Question
The question asks us to determine which shapes have the same area. At first glance, this might seem a bit tricky, but don’t worry – we’ll break it down step by step.
Calculating the Area of Shape E
Let’s start by looking at shape E. It’s a triangle, and we know that the area of a triangle is calculated using the formula:
Area = (base × height) ÷ 2
If shape E were a full square, it would have an area of 4 square units (2 × 2). However, since it’s a triangle, we need to divide that by 2. Therefore, the area of shape E is 2 square units.
Calculating the Area of Shape A
Now, let’s move on to shape A. This shape is a parallelogram. We can see that it consists of one whole square and two half squares. When we put those half squares together, they make another whole square. So, the area of shape A is also 2 square units.
Calculating the Area of Shape B
Shape B is similar to shape A. It also consists of two whole squares, giving it an area of 2 square units as well.
So far, we’ve discovered that shapes A, B, and E all have an area of 2 square units.
Calculating the Area of Shape D
Shape D is a bit trickier. To calculate its area, we can break it down by drawing lines to complete the partial squares. We have one whole square and another half square, giving shape D a total area of 1.5 square units.
Calculating the Area of Shape C
Lastly, let’s look at shape C. By drawing lines to complete the squares, we can see that it consists of two whole squares and one half square. This gives shape C a total area of 2.5 square units.
Answering this CSSE Area and Perimeter Question
Now that we’ve calculated the areas of all the shapes, we can answer the question: Which shapes have the same area?
The answer is shapes A, B, and E. They all have an area of 2 square units. It’s important to note that if you only wrote two of the three shapes, you wouldn’t get full marks for this question. Make sure to include all three: A, B, and E.
Bonus: Perimeter
The question also asks about the shapes that have the same perimeter. This can be a bit more challenging, so let’s tackle it together.
For shape A, we have 4 units plus 2 diagonals. It’s important to remember that diagonals are not the same as vertical or horizontal lines of 1 unit.
Shape B has a perimeter of 6 units.
Shape C is a bit trickier. It has 4 units plus 3 diagonals.
Shape D has 2 units plus 3 diagonals.
Finally, shape E has 4 units plus 2 diagonals.
After analyzing all the shapes, we can see that shapes A and E have the same perimeter. They both have 4 vertical or horizontal lines and 2 diagonals.
Conclusion
In this CSSE Area and Perimeter video, we’ve learned how to calculate the area and perimeter of various shapes in a grid. We discovered that shapes A, B, and E have the same area of 2 square units, while shapes A and E have the same perimeter of 4 units plus 2 diagonals.
Remember, when answering questions like this, it’s essential to:
- Break down the shapes into familiar components (squares, triangles, etc.)
- Use the appropriate formulas for area and perimeter
- Include all the shapes that satisfy the question’s requirements
By following these steps and practising regularly, you’ll be well-equipped to tackle similar CSSE Area and Perimeter questions in your exams. Keep up the great work, and happy learning!
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