Respuesta :
The area of the quadrilateral increases as the lengths of the sides become
the same.
- Arun made the shape (square) with the greatest area
Reasons:
Length of the wire = 32 cm
Length of side of square Arun made, s = 8 cm
Perimeter of the square, P = 4 × 8 cm = 32 cm = Length of the wire
- Area of the square Arun made, A = s² = 8 cm × 8 cm = 64 cm²
Length of a side of the rectangle David made, L = 9 cm
Perimeter of the rectangle, P = 32 cm = 2·L + 2·B
Where;
B = The breadth of the rectangle
Therefore;
P = 32 cm = 2·L + 2·B = 2 × 9 cm + 2·B
2·B = 32 cm - 2 × 9 cm = 14 cm
B = 14 cm ÷ 2 = 7 cm
The breadth of the rectangle David made B = 7 cm
Therefore;
- The area of the rectangle David made, A = 9 cm × 7 cm = 56 cm²
Breadth of the rectangle Raj made, B = 10 cm
Therefore;
32 cm = 2·L + 2 × 10 cm
2·L = 32 cm - 2 × 10 cm = 12 cm
L = 12 cm ÷ 2 = 6 cm
The length of the rectangle Raj made, L = 6 cm
- Area of the rectangle Raj made, A = 10 cm × 6 cm = 60 cm²
Therefore;
- The square made by Arun that has an area of 64 cm² is the shape with the greatest area.
Learn more about the area of plane shapes here:
https://brainly.com/question/8370300
