Question

Основание прямоугольника равно 10м высота 14 м из него вырезан прямоугольный треугольник с катетами 8м 6м гипотенузой 10м Определите площадь и периметр полученной фигуры

Answer 1

Ответ:

$116m^{2}, \quad 44m;$

Пошаговое объяснение:

Площадь прямоугольника:

$S_{1}=a_{1} \cdot b_{1};$

Площадь прямоугольного треугольника:

$S_{2}=\frac{1}{2} \cdot a_{2} \cdot b_{2};$

Площадь фигуры, полученной путём вырезания прямоугольного треугольника из прямоугольника, равна:

$S_{3}=S_{1}-S_{2}=a_{1} \cdot b_{1}-\frac{1}{2} \cdot a_{2} \cdot b_{2};$

$S_{3}=10 \cdot 14-\frac{1}{2} \cdot 8 \cdot 6-140-4 \cdot 6=140-24=116(m^{2});$

Периметр полученной фигуры:

$P_{3}=10+14+(10-6)+10+(14-8)=24+4+10+6=34+10=44(m);$

Answer 2

Calculation of the Area and Perimeter of the Figure

To determine the area and perimeter of the figure obtained by cutting a right triangle from a rectangle, we need to calculate the areas and perimeters of both shapes separately and then subtract the area of the triangle from the area of the rectangle.

Let's start by calculating the area and perimeter of the rectangle.

Rectangle: - Base: 10 m - Height: 14 m

The area of a rectangle is calculated by multiplying its base by its height: Area = base * height. Therefore, the area of the rectangle is Area = 10 m * 14 m = 140 m². The perimeter of a rectangle is calculated by adding the lengths of all its sides: Perimeter = 2 * (base + height). Therefore, the perimeter of the rectangle is Perimeter = 2 * (10 m + 14 m) = 2 * 24 m = 48 m. Now, let's calculate the area and perimeter of the right triangle.

Right Triangle: - Cathetus 1: 8 m - Cathetus 2: 6 m - Hypotenuse: 10 m

The area of a right triangle is calculated by multiplying the lengths of its two catheti and dividing the result by 2: Area = (cathetus1 * cathetus2) / 2. Therefore, the area of the right triangle is Area = (8 m * 6 m) / 2 = 48 m². The perimeter of a right triangle is calculated by adding the lengths of its three sides: Perimeter = cathetus1 + cathetus2 + hypotenuse. Therefore, the perimeter of the right triangle is Perimeter = 8 m + 6 m + 10 m = 24 m. Finally, to find the area and perimeter of the obtained figure, we subtract the area of the triangle from the area of the rectangle and add the perimeters of both shapes:

Area of the Figure = Area of the Rectangle - Area of the Triangle = 140 m² - 48 m² = 92 m².

Perimeter of the Figure = Perimeter of the Rectangle + Perimeter of the Triangle = 48 m + 24 m = 72 m.

Therefore, the area of the obtained figure is 92 m² and the perimeter is 72 m.

I hope this helps! Let me know if you have any further questions.