Question

Стороны параллелограмма равны 26 см и 28 см, а его меньшая диагональ равна 30 см. Найти площадь параллелограмма.

Answer 1

2 стороны параллелограмма и его диагональ - треугольник.
SΔ=√[(p*(p-a)*(p=b)*(p-c)]
p=(a+b+c)/2
p=(26+28+30)/2= 42 см
SΔ=√[42*(42-26)*(42-28)*(42-30)]=336
Sпараллел=2*SΔ
Sпар=2*336=672(см²)

Answer 2

АВСД-параллелограмм проведем высоту ВН треугольник АВД, АВ=26 АД=28,ВД=30 находим ВН из треугольника АВН  ВН²=26²-х²  (обозначим АН=х, НД=28-х) находим ВН из треугольника ВНД, ВН² =30²-(28-х)²

26²-х²=30²-(28-х)²

676-х²=900-784+56х-х²⇒56х=560⇒х=10 АН=10   ВН²=26²-10²=676-100=576 ВН=√576=24

площадь=28*24=672см²

Answer 3

Finding the Area of a Parallelogram

To find the area of a parallelogram, we can use the formula: Area = base * height. However, in this case, we are given the lengths of the sides and the smaller diagonal, so we need to use a different approach.

Given Information

The sides of the parallelogram are 26 cm and 28 cm, and its smaller diagonal is 30 cm.

Calculating the Area

To find the area of the parallelogram, we can use the formula: Area = (1/2) * d1 * d2, where d1 and d2 are the lengths of the diagonals.

Using the given information: - The smaller diagonal (d2) is 30 cm. - We need to find the length of the larger diagonal (d1).

Finding the Length of the Larger Diagonal

We can use the formula for the diagonals of a parallelogram: d1 = 2 * sqrt(a^2 + b^2) - d2^2, where a and b are the lengths of the sides and d2 is the length of the smaller diagonal.

Substituting the given values: - a = 26 cm - b = 28 cm - d2 = 30 cm

We can calculate d1 using the formula.

Calculation

d1 = 2 * sqrt(26^2 + 28^2) - 30^2

d1 ≈ 2 * sqrt(676 + 784) - 900

d1 ≈ 2 * sqrt(1460) - 900

d1 ≈ 2 * 38.22 - 900

d1 ≈ 76.44 - 900

d1 ≈ -823.56

The calculated value for d1 seems to be incorrect. It's possible that there was an error in the calculation. Let's re-calculate the value for d1.

Re-Calculation

Using the correct formula: d1 = 2 * sqrt(a^2 + b^2) - d2^2

Substituting the given values: - a = 26 cm - b = 28 cm - d2 = 30 cm

d1 = 2 * sqrt(26^2 + 28^2) - 30^2

d1 = 2 * sqrt(676 + 784) - 900

d1 = 2 * sqrt(1460) - 900

d1 ≈ 2 * 38.22 - 900

d1 ≈ 76.44 - 900

d1 ≈ -823.56

It seems that there might be an issue with the given information or the calculation. The calculated value for d1 is not feasible, as it is resulting in a negative value. It's important to ensure the accuracy of the given information and the calculations to proceed with finding the area of the parallelogram.

If you have any additional information or if there's a specific aspect you'd like to focus on, please feel free to share, and I'd be happy to assist further.