Let length of AG and BF be 1 unit each.

Then BE = BC = CD = ED = 1 unit + 8cm

Perimeter of rectangle

= AB + GF + AG + BF
= AB + GF + 1 unit + 1 unit
= AB + GF + 2 units

Perimeter of square

= (1 unit + 8cm) × 4
= 4 units + 32cm


So AB + GF + 2 units = 4 units + 32cm

Comparing the two,


AB + GF = 2 units + 32cm

Since AB = GF, each of them = 1 unit + 16cm


Then AC = AB + BC
= 1 unit + 16cm + 1 unit + 8cm
= 2 units + 24 cm

2 units + 24cm = 52cm

2 units = 28cm

1 unit = 14cm


AB = 14cm + 16cm = 30cm
BC = 14cm + 8cm = 22cm

Area of figure

= Area of rectangle + area of square
= 30cm × 14cm + 22cm × 22cm
= 420cm² + 484cm²
= 904cm²

A faster way using logic :

If 1 side of the square is longer than 1 breadth of the rectangle by 8cm,

Then 2 sides of the square are longer than 2 breadths of the rectangle by 16cm.

Since the perimeters are the same,

then the 2 lengths of the rectangle must be longer than 2 sides of the square by 16cm.

So 1 length of the rectangle must be longer than 1 side of the square by 8cm.


Then 52cm
= 1 length of rectangle + 1 side of a square
= 2 sides of a square + 8cm

52cm - 8cm = 44cm
44cm ÷ 2 = 22cm (1 side of a square)