Answer:
I will answer everithing in terms of a and b.
The area of a square is equal to L*L = L^2
where L is the lenght of the side of a square.
The area of a triangle is equal to b*h/2
where b is the base of the triangle and h is the heigth.
1) Area of the triangles in the first image.
The area of one triangle is: a*b/2
then for the 4 triangles we have 4 times that amount:
Area = 4*(a*b/2) = 2*a*b
2) For the triangles in the second image we have the same situation the base is a and the heigth is b, so the area for the 4 triangles is:
Area = 4*(a*b/2) = 2*a*b
3) The unshaded area in the first image is:
Area = c*c = c^2
And, by the Pythagorean theorem we have that:
b^2 + a^2 = c^2
Then the area of the square is:
Area = c^2 = a^2 + b^2
4) the combined areas from the two squares in image 2 are:
Area of the big one = b*b = b^2
Area of the small one = a*a = a^2
total area: a^2 + b^2
5) The total area for the two images will be:
Total area for both images = a^2 + b^2 + a^2 + b2 = 2*(a^2 + b^2)
