Break the shape into smaller shapes that you know the perimeter of.
In this case, the larger shape can be broken into a 8cm X 5cm rectangle and a right triangle with a height of 5cm and a base of 5cm (The length of the base is not directly given. We have to calculate it and we obtain it as 8cm - 1cm - 2cm = 5cm).
Therefore, the total area = area of the rectangle + area of the triangle = 40 sq. cm + 12.5 sq. cm = 52.5 sq cm
To find the perimeter, we can add the perimeters of the two shapes but we have to subtract the overlapping segment that is counted twice.
To calculate the perimeter of the triangle, we need the length of the hypotenuse which we can get using the Pythagorean theorem.
Therefore, perimeter = perimeter of the rectangle + perimeter of the triangle - 10cm (2 x 5cm) = 26cm + 10cm + 5 x sqrt(2) cm - 10cm = 26cm + 5 sqrt(2) cm.