All Tasks - Asymptote

Dato il trapezio $ABCD$, sappiamo che la somma delle sue basi è $AD+BC=42 cm$. Sapendo che la sua altezza è congruente al lato del rombo $EFGH$ avente il perimetro di $136 cm$. Calcolare l'area del trapezio.

Calcolare la base del triangolo $EGF$, equivalente al quadrato $ABCD$. Sapendo che il perimetro del quadrato è $280 cm$ e l'altezza del triangolo è congruente ai $\frac{7}{5}$ del lato del quadrato.

Written with this little fancy three up in the air, the cube of a number is simply this number multiplied by itself twice. For example $2^3=2\times 2\times 2=8$. Compute the cube of the following numbers:

Look at these cubes, of size 1, 2, 3,... Suppose they are made of squares, all of the same unit height. How can you spread these squares on the plane? If you have 10 cubes, what is the area tiled by all these cubes?

Look at these pyramids. They are made of square pieces, all of the same height, which is the depth of each step. Hence their volume is the sum of the squares. You have six of them to make a cuboid. If there are ten stairs, what is the size of this cuboid made of the six pyramids?

Now, let's turn our attention to the corners, the turning points, alternating bottom-left, top-left, top-right and bottom-right, beginning with 1, 2, 3, 5, 7...