Answer:
a) A₁ = 18 unit²
b) A₂ = 20 unit²
c) A₃ = 12 unit²
d) A₄ = 12 unit²
Explanation:
a) Given that the side length of square is 6 units, we have;
The height of the square = The height of the triangle = 6 units
The base of the triangle = The side length of the square = 6 units
The area of a triangle A₁ = 1/2×base×height = 1/2×6×6 = 18 unit²
b) The side of the square A₂ forms an hypotenuse side to the side length 2 and 4 on sides of the circumscribing square
The length of the side = √(4^2 + 2^2) = 2·√5
A₂ = The area of a square =Side² = (2·√5)² = 20 unit²
c) The base length of the triangle, A₃ + 2 = The side length of the circumscribing square = 6 units
∴ The base length of the triangle, ₃₂ = 6 - 2 = 4 units
The height of the triangle, A₃ = The side length of the circumscribing square = 6 units
The area of a triangle A₃ = 1/2×base×height = 1/2×4×6 = 12 unit²
d) Figure, A₄, is a parallelogram;
The area of a parallelogram = Base × Height
The base of the parallelogram, A₄ + 4 = 6 units
Therefore, the base of the parallelogram, A₄ = 6 - 4 = 2 units
The height of the parallelogram = The side length of the circumscribing square = 6 units
The area of a parallelogram A₄ = 2× 6 = 12 unit².