The expression for the area is a^2 + b^2 + 2ab
How to determine the area expression?
The attached image represents the missing information in the question
From the attached image, we have:
- Square: Dimension = c by c
- Triangles: Dimension = Base a or b and Height b or a
The area of the square is calculated using:
Area = c * c
Area = c^2
The area of the four triangles is:
Area = 4 * 0.5 * Base * Height
Area = 4 * 0.5 * b * a
This gives
Area = 2ab
When the areas of the square and the triangles are added, we have:
Total = c^2 + 2ab
Also, we have:
c^2 = a^2 + b^2 ---- Pythagoras theorem
So, we have:
Total = a^2 + b^2 + 2ab
Hence, the expression for the area is a^2 + b^2 + 2ab
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