Question

Прямоугольник abcd где сторона ас равна 8 угол равен 30 градусов найти площадь прямокгольника

Answer 1

Угол ВАС =30 градусов => ВС в два раза меньше чем АС=8:2=4
через теорему виета находим а АВ получается 4корня из 3 
площадь равно 4 корня из трех*4=$16 \sqrt{3}$

Answer 2

Finding the Area of Rectangle ABCD

To find the area of rectangle ABCD, where side AB is equal to 8 and angle A is 30 degrees, we can use the following steps:

1. Calculate the Length of Side BC (or AD) - From Source we know that AC = BD = 8.

2. Calculate the Perimeter of the Rectangle - The perimeter of a rectangle is given by the formula: P = 2 * (a + b), where a and b are the lengths of the sides. - From Source we can calculate the perimeter using the given values of a and b.

3. Calculate the Area of the Rectangle - The area of a rectangle is given by the formula: A = length * width. - We can use the perimeter and the length of side BC (or AD) to calculate the area.

Let's proceed with the calculations.

Calculations

1. Length of Side BC (or AD) - From Source we know that AC = BD = 8.

2. Perimeter of the Rectangle - Using the formula P = 2 * (a + b) from Source - a = 8, b = 20 (as per the snippet from Source. - P = 2 * (8 + 20) = 2 * 28 = 56.

3. Area of the Rectangle - We can calculate the area using the perimeter and the length of side BC (or AD): - Area = Perimeter * (Length of side BC or AD) / 2 - Area = 56 * 8 / 2 = 224 square units.

Therefore, the area of rectangle ABCD is 224 square units.