Question

ПОМОГИТЕ СРОЧНО!!!Меньшая основа и боковая сторона прямоугольной трапеции равна а см, а один из углов 45 градусов. Найти площадь трапеции.

Answer 1

Чертеж во вложении.
1) Проведем СС1⊥ AD
2) По условию CD=а, угол D=45, значит $sinD= \frac{CC1}{CD}= \frac{CC1}{a}$
=>$CC1=sin45*a$
3) Рассмотрим ∆ СС1D: он прямоуг, угол D=45=> СС1=С1D=sin45*a
4) Т.к.СС1-высота, то ВС=АС1=а. AD=AC1+C1D= a+sin45*a
5) Sabcd=1/2*CC1*(BC+AD)=1/2*sin45*a*(a+a+sin45*a)=1/2*sin45*a*(2a+sin45*a)=1/2*sin45*a*a(2+sin45)=1/2*a^2*sin45(2+sin45)=1/2*a^2*(sin45*2+0,5)=sin45*a^2+0,25a^2
Ответ: sin45* a^2+0,25a^2

Answer 2

Calculation of the Trapezoid Area

To find the area of a trapezoid, we need to know the lengths of the bases and the height. In this case, we are given that the smaller base and one of the side lengths of the trapezoid are both equal to 'a' cm, and one of the angles is 45 degrees.

Let's denote the smaller base as 'a', the larger base as 'b', and the height as 'h'. We can use the formula for the area of a trapezoid:

Area = (a + b) * h / 2

Since we are given that the smaller base and one of the side lengths are equal to 'a' cm, we can substitute 'a' for both the smaller base and the side length in the formula.

Now, we need to find the value of 'b' and 'h' to calculate the area.

Finding the Value of 'b'

Unfortunately, the given information does not provide enough details to determine the value of 'b'. We only know that the smaller base and one of the side lengths are equal to 'a' cm, but we don't have any information about the larger base. Therefore, we cannot calculate the exact value of the area without knowing the value of 'b'.

If you have any additional information or measurements, please provide them so that we can assist you further in finding the area of the trapezoid.