The perimeter of the square is 52 decimetres, which will be equal to the area of the square if its side is increased by 30 cm.

Given:
a1 =? cm; a2 = 30 cm more;
P1 = 52 dm; P2 =? cm;
S1 =? cm², S2 =? cm².
The task of calculating the perimeter and area of a square. The perimeter of the square is calculated by the formula: P = 4 * a – where, a is the side of the square. The area of a square is calculated by the formula:
S = a² – where, and – the side of the square.

We calculate the side of the square using the formula: a = P: 4
1) a1 = 52: 4 = 13 (cm);

We calculate the side of the square if its side is increased by 30 cm
2) a2 = 13 + 30 = 43 (cm);
3) S2 = a² = 43² = 1849 (cm²);
Answer: 1849 cm² will be equal to the area of a square if its side is increased by 30 cm.