Answer:
Part a : 20 units², Part d : 12 units²
Explanation:
We are given that the side lengths of each square is 6 units. In this case we can calculate the area of the triangles, subtracting from the area of the outer square, such that we calculate the remaining, area of the shaded region / inscribed square.
Area of Outer Square ( Same in all Cases ) = 6
6 = 36 units²,
Area of Common Triangles ( 4 Triangles ) = 1 / 2
Base
Height = 1 / 2
2
( 6 - 2 ) = 1 / 2
2
4 = 4,
4
4 = 16 units²
Area of inscribed Square = 36 units² - 16 units² = 20 units²
For this second case the inscribed shape is not a square, but it can be calculated through a similar approach,
Area of Outer Square ( Same in all Cases ) = 6
6 = 36 units²,
Area of Common Triangles ( 2 Triangles ) = 1 / 2
Base
Height = 1 / 2
4
6 = 2
6 = 12,
12
2 = 24 units²
Area of inscribed shape = 36 units² - 24 units² = 12 units²