Question

диагональ ВД параллелограмма АВСД перпендикулярна к стороне АД, Ав= 12 см, угол А= 45 градусов. найти площадь параллелограмма.

Answer 1

ΔАВД равнобедренный, ДД₁-высота на основание АВ, т.к. Δ равнобедренный, то ВД₁=Д₁А=12/2=6

ДД₁=6 (ΔДД₁А- равнобедренный, угол А=45, угол АД₁Д=90)

S=ДД₁*АВ=6*12=72

Answer 2

Calculation of the Parallelogram's Area

To find the area of a parallelogram, we need to know the length of one of its sides and the length of the perpendicular drawn from that side to the opposite side. In this case, we are given that side AD is perpendicular to side AB, with a length of Av = 12 cm, and angle A = 45 degrees.

To calculate the area of the parallelogram, we can use the formula:

Area = base * height

In a parallelogram, any side can be considered as the base, and the perpendicular drawn from that side to the opposite side is the height.

Let's calculate the area using the given information:

Base = AD = Av = 12 cm

Height = AB

To find the height, we can use trigonometry. Since angle A = 45 degrees, we can use the sine function to find the height:

sin(A) = opposite / hypotenuse

In this case, the opposite side is the height (AB) and the hypotenuse is the base (AD).

sin(45) = AB / AD

Simplifying the equation:

AB = AD * sin(45)

Now we can substitute the values and calculate the height:

AB = 12 cm * sin(45)

Using a calculator, we find that sin(45) is approximately 0.7071. Substituting this value:

AB = 12 cm * 0.7071

AB ≈ 8.4853 cm

Now we have the base (AD) and the height (AB), so we can calculate the area:

Area = AD * AB

Substituting the values:

Area = 12 cm * 8.4853 cm

Area ≈ 101.8236 cm²

Therefore, the approximate area of the parallelogram ABCD is 101.8236 cm².

Please note that the calculations are approximate due to rounding.