6th grade Q3

To solve problems involving the area of composite figures, here’s a step-by-step guide that you can follow:

1. Understand the problem: Carefully read the problem and identify what shapes make up the composite figure.
2. Break down the composite shape: Separate the composite figure into familiar shapes (triangles, rectangles, circles, etc.) that you know how to calculate the area for.
3. Identify given information and needed calculations: For each shape, decide on the formula you’ll use (e.g., area of a rectangle = length × width).
4. Calculate the area of each individual shape: Use the formulas to calculate the area of each individual shape.
5. Add or subtract areas as needed
   • Adding Areas: If the composite shape is a combination of shapes joined together, add the areas of each part to get the total area.
   • Subtracting Areas: If the composite shape has a cut-out shape, calculate the area of the entire larger shape and subtract the area of the part that’s missing.

Example:

A swimming pool measures 5x10 meters. A 1-meter-wide concrete pathway surrounds the edges of the swimming pool. What is the area of the pathway?

To solve this problem, you need to find the area of the concrete pathway surrounding the swimming pool. First, calculate the area of the swimming pool itself. The pool is a rectangle with dimensions 5 meters by 10 meters. The area of the pool is given by the formula for the area of a rectangle:

Next, consider the entire area including the pool and the surrounding pathway. Since the pathway is 1 meter wide, the total dimensions including the pathway are 7 meters by 12 meters (adding 1 meter to each side of the pool's length and width). Calculate the area of this larger rectangle:

Finally, to find the area of just the pathway, subtract the area of the pool from the area of the pool with the pathway:

Thus, the area of the concrete pathway is $34{\text{m}}^2$.