If 1 cuboid can be cut into exactly three cubes, then two sides are squares, and the aspect ratio of the other four sides is 1:3. So the surface area of a cuboid can be regarded as the area of 14 squares (that is, one side of it and one side of the cut cube).

The square area is 420/ 14 = 30 square centimeters.

The surface area of the cube is 30× 6 = 180 cm2.

Two questions

Let a small rectangle have a length of a and a width of b.

Then 2a = 3b, and it can be seen from the figure that a+b = 10.

The solution is a = 6 and b = 4.

Large rectangular area = 5 small rectangular areas = 5× 6× 4 = 120.

Three questions

Left 1→ right 2

Left 2→ Right 3

Left 3→ right 1

Four questions

Shadow area = "sum of two squares" minus "three small triangles"

Because you didn't give the area of the big square, the answer is unknown, so I'll just give you an idea.

Five questions

Given the height and area of the parallelogram, the length of the base can be calculated as 54/6 = 9 cm.

Because that angle is 45, the radius of the circle should be 9-6 = 3 cm.

According to the trigonometric function, the sine value of the smaller acute angle of the shadow part is 3/6 = 0.5, that is, the smaller acute angle is 30, and the height of the shadow part is twice that of the root number 3.

So the shadow area is 0.5×6×2 times the root number 3 = 6 times the root number 3.