Question

Диагональ AC прямоугольника ABCD равна 3 см, и составляет со стороной AD угол 45 градусов. Найти площадь ABCD?

Answer 1

если угол САД=45, то угол САВ = 90-45=45, тогда АВСД - квадрат, тогда

Sквадр = 1/2 * d1*d2=1/2*3*3=4,5 см2

 

Answer 2

 

ADC  равнобедренный , значит   AD=DC

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Answer 3

Calculation of the Area of Rectangle ABCD

To find the area of rectangle ABCD, we need to know the length of its sides. We are given that the diagonal AC of the rectangle is 3 cm and forms a 45-degree angle with side AD.

Let's denote the length of side AD as x. Since the diagonal AC forms a 45-degree angle with side AD, we can use the properties of a 45-45-90 triangle to find the length of side AD.

In a 45-45-90 triangle, the length of the hypotenuse (diagonal AC) is equal to √2 times the length of each leg (side AD). Therefore, we have:

AC = √2 * AD

Substituting the given values, we get:

3 = √2 * x

To solve for x, we can square both sides of the equation:

3^2 = (√2 * x)^2

9 = 2 * x^2

Dividing both sides by 2, we have:

x^2 = 4.5

Taking the square root of both sides, we find:

x = √4.5

Therefore, the length of side AD is approximately 2.12 cm.

Now that we know the lengths of sides AD and AC, we can calculate the area of rectangle ABCD using the formula:

Area = Length * Width

Area = AD * AC

Substituting the values, we get:

Area = 2.12 cm * 3 cm

Area = 6.36 cm^2

Therefore, the area of rectangle ABCD is approximately 6.36 square centimeters.

Please note that the calculations are approximate due to rounding.

Answer

The area of rectangle ABCD is approximately 6.36 square centimeters.