For the figures below, assume they are made of semicircles, quarter circles and squares. for each shape, find the area and perimeter. give your answer as a completely simplified exact value in terms of π (no approximations).

1. Area of the first figure;
Area of the quarter circle = 1/4 πr²
= 1/4π 12²
= 36π cm²
Area of the triangle = 1/2×base×height
 = 1/2 × 12×12
 = 72 cm²
Thus the area of the region
  = (36π-72) cm²

2. Perimeter of the first figure
The length of the arc AC is 2πr/4
 = 2π×12/4
 = 6π cm
the length of line AC
√(12² +12²) = 16.97
Thus the perimeter of the figure
  = (6π+16.97) cm

3. The are of figure 2
Area of the semi circle πr²/2
= 12²π/2 = 72π cm²
The area of the square
= 24 × 24 =576 cm²
 Area of the semi circle = 72 π cm²
Thus the area of the part of the square
= (576-72π) cm²
total area 
72π +576-72π
= 576 cm²

4. Perimeter of figure 2
The length of arc AD = (2πr)/2
 = 2π×12/2 = 12π cm
but length of arc AD is equal to that of arc BC
Thus arc BC = 12πcm
Therefore, total perimeter
= 12π +12π +24 +24
= (24π +48) cm

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