QuestionCalcola perimetro e area di un trapezio isoscele con lati $25 \mathrm{~cm}$ , altezza $24 \mathrm{~cm}$ e base minore $16 \mathrm{~cm}$ .

Studdy Solution

STEP 1

Assumptions1. The oblique side of the isosceles trapezoid measures $25 \mathrm{~cm}$ . The height to the smaller base measures $24 \mathrm{~cm}$
3. The smaller base measures $16 \mathrm{~cm}$
4. The trapezoid is isosceles, which means the two oblique sides are equal in length

STEP 2

First, we need to find the length of the larger base. We can do this by using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is the oblique side of the trapezoid, one side is the height, and the other side is half the difference between the larger and smaller bases.
$(Base\, maggiore - Base\, minore)/2 = \sqrt{ato\, obliquo^2 - Altezza^2}$

STEP 3

Now, plug in the given values for the oblique side, the height, and the smaller base to calculate the half difference between the larger and smaller bases.
$(Base\, maggiore -16\, cm)/2 = \sqrt{25\, cm^2 -24\, cm^2}$

STEP 4

Calculate the half difference between the larger and smaller bases.
$(Base\, maggiore -16\, cm)/2 = \sqrt{625\, cm^2 -576\, cm^2}$

STEP 5

Continue the calculation.
$(Base\, maggiore -16\, cm)/2 = \sqrt{49\, cm^2}$

STEP 6

Take the square root.
$(Base\, maggiore -16\, cm)/2 =\, cm$

STEP 7

olve for the larger base.
$Base\, maggiore =2 \times7\, cm +16\, cm =30\, cm$

STEP 8

Now that we have the lengths of the smaller base, the larger base, and the oblique side, we can calculate the perimeter of the trapezoid.
$Perimetro = Base\, minore + Base\, maggiore +2 \times Lato\, obliquo$

STEP 9

Plug in the values to calculate the perimeter.
$Perimetro =16\, cm +30\, cm +2 \times25\, cm$

STEP 10

Calculate the perimeter.
$Perimetro =16\, cm +30\, cm +50\, cm =96\, cm$

STEP 11

Now, we can calculate the area of the trapezoid. The formula for the area of a trapezoid is $Area = \frac{}{} \times (Base\, minore + Base\, maggiore) \times Altezza$

STEP 12

Plug in the values to calculate the area.
$Area = \frac{}{2} \times (16\, cm +30\, cm) \times24\, cm$

STEP 13

Calculate the area.
$Area = \frac{}{2} \times46\, cm \times24\, cm =552\, cm^2$ The perimeter of the trapezoid is $96 \mathrm{~cm}$ and the area is $552 \mathrm{~cm}^2$ .

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