The figure is made up of 3 identical rectangles. The perimeter of the figure is 60 cm. What is the area of 1 rectangle? Ans: ___ cm$^2$

1. Establish the relationship between the length and breadth of the rectangle from the figure

From the figure, the length of the vertical rectangle is equal to the combined width of the two horizontal rectangles.
Let the breadth of one rectangle be $b$.
Then the length of one rectangle is $l = 2b$.

2. Express the perimeter of the figure in terms of the breadth

The perimeter of the figure consists of:

• Top edge: $l + b = 2b + b = 3b$
• Bottom edge: $l + b = 2b + b = 3b$
• Left edge: $2b$
• Right edge: $l = 2b$
  Total perimeter = $3b + 3b + 2b + 2b = 10b$

3. Solve for the breadth and length

Given perimeter = $60$ cm.
$10b = 60$
$b = 6$ cm
Length $l = 2b = 2(6) = 12$ cm

4. Calculate the area of 1 rectangle

Area of 1 rectangle = $l \times b = 12 \times 6 = 72$ cm$^2$