Question

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

Answer 1

The perimeter cannot be calculated with the given measurements as they do not form a right trapezoid.

Step-by-step explanation:

Perimeter of a trapezoid:

The perimeter of a trapezoid is calculated by adding the lengths of all its sides. In this case, the trapezoid has two bases, measuring 74 cm and 14 cm, and the height is 32 cm.

The formula for calculating the perimeter is: P = a + b + c + d, where a and b are the lengths of the bases, and c and d are the lengths of the non-parallel sides. In a right trapezoid, the non-parallel sides are equal in length, so c = d.

Using the given values:

• a = 74 cm
• b = 14 cm
• c = d (non-parallel sides)
• h = 32 cm (height)

Substituting the values into the formula, we have: P = 74 + 14 + c + c. Simplifying the equation gives P = 88 + 2c.

To find the value of c, we can use the Pythagorean theorem. The two non-parallel sides, c and d, along with the height, form a right triangle.

Using the Pythagorean theorem, we have: c^2 + h^2 = d^2. Substituting the values, we get c^2 + 32^2 = d^2. Simplifying the equation gives c^2 + 1024 = d^2.

Since c = d in a right trapezoid, we can replace d with c in the equation: c^2 + 1024 = c^2. Subtracting c^2 from both sides gives 1024 = 0, which is not true.

This means that the given measurements do not form a right trapezoid, as the Pythagorean theorem is not satisfied. Therefore, we cannot calculate the perimeter using the given values.

Answer 2

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