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Calculați aria unui trapez oarecare cu bazele de 4 cm și 18 cm, iar laturile laterale de 13 cm și 15 cm. Vă rog repede.

Answer :

Answer:

132 cm²

Step-by-step explanation:

h² = 13² - x²

h² = 15² - (14 - x)²

169 - x² = 225 - (196 - 28x + x²) = 29 + 28x -x²

28x = 169 - 29 = 140

x = 5

h = √13² - x² = √169 - 25=√144 = 12

Area of Trapezoid: (4 + 18) x 12 / 2 = 132

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Rewritten by : Barada

The area of the trapezoid is 22√30 square centimeters.

To find the area of a trapezoid, you can use the formula:

Area = (1/2) * (sum of the lengths of the bases) * (height)

In your case, the bases are 4 cm and 18 cm, and the height is not given. To calculate the height, you can use the Pythagorean theorem, as the trapezoid can be divided into a rectangle and two right triangles.

First, calculate the length of the trapezoid's altitude (height):

Height^2 = Side^2 - (1/2 * Base Difference)^2

Height^2 = 13^2 - (1/2 * (18 - 4))^2

Height^2 = 169 - (1/2 * 14)^2

Height^2 = 169 - 7^2

Height^2 = 169 - 49

Height^2 = 120

Height = √120

Height = 2√30 cm

Now that you have the height, you can find the area of the trapezoid:

Area = (1/2) * (4 + 18) * 2√30

Area = (1/2) * 22 * 2√30

Area = 22√30 square cm

So, the area of the trapezoid is 22√30 square centimeters.

for such more question on trapezoid

https://brainly.com/question/1410008

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