Un trapezio rettangolo ha le basi di 74 cm e 14 cm e l'altezza di 32 cm. Calcola il perimetro del trapezio.

Answer: The perimeter is 175.6cm

Step-by-step explanation:

This can be translated to:

A rectangular trapeze has a base of 74 cm and a base of 14 cm and a height of 32 cm. Calculate the perimeter of the trapeze.

We can form a triangle rectangle in the trapezoid, where the base will be equal to half of the difference between the two bases, this is:

B = (74cm - 14cm) / 2 = 30cm

So 30 cm is one cathetus of the triangle rectangle, the other cathetus is the height of the trapeze, this is 32cm.

Then the hypotenuse is equal to, by Pythagoras theorem:

H = √ ((30cm) ^2 + (32cm) ^2) = 43.8 cm

Then, the hypotenuse is the length of the tilted side of the trapeze, (and we have two of those)

Then the perimeter of the trapeze is:

P = B + b + 2*H

where B is the larger base, b is the smaller base, and H is the length of the tilted sides.

P = 74cm + 14cm + 2 * (43.8cm) = 175.6cm