Question

Стороны параллелограмма равны 4 и 13, а диагональ 15. Найдите его площадь.

Answer 1

Ответ: 48 см²

Объяснение:

Диагональ параллелограмма делит его на два равных треугольника.

Рассмотрим один из них: его стороны 4 ,13 и 15. Найдём его площадь по формуле Герона: S Δ=√(р(р-а)(р-в)(р-с)).

P Δ=4+13+15=32 (см),  р=Р:2=32:2=16 (см).

S Δ=√(16*(16-4)(16-13)(16-15))=√16*12*3*1=√16*36=4*6=24 (см²).

S= SΔ *2= 24*2= 48 (см²)

Answer 2

To find the area of a parallelogram, we can use the formula:

Area = base × height

In a parallelogram, the base and height are perpendicular to each other. In this case, the two sides of the parallelogram are given as 4 and 13, and the diagonal is given as 15.

Let's label the sides of the parallelogram as follows: Base = 13 (one of the given sides) Height = 4 (the other given side) Diagonal = 15 (the given diagonal)

Now, we can find the height of the parallelogram using the Pythagorean theorem since the diagonal, base, and height form a right-angled triangle.

Using the Pythagorean theorem: Height² + Base² = Diagonal² Height² + 13² = 15² Height² + 169 = 225 Height² = 225 - 169 Height² = 56 Height = √56 ≈ 7.48 (rounded to two decimal places)

Now that we have the height, we can calculate the area of the parallelogram: Area = Base × Height Area = 13 × 7.48 ≈ 97.24 square units (rounded to two decimal places)

So, the area of the parallelogram is approximately 97.24 square units.