Question

найдите площадь равнобедренной трапеции,если ее меньшее основание равно 18см, высота 9см и острый угол равен 45 градусам

Answer 1

большее основание =18+9+9=36

площадб равна ((большее основание+меньшее основание)/2)*высоту= (36+18)/2*9=243см

Answer 2

Calculation of the Area of an Isosceles Trapezoid

To find the area of an isosceles trapezoid, we can use the formula:

Area = (a + b) * h / 2

where: - a and b are the lengths of the bases of the trapezoid - h is the height of the trapezoid

In this case, the smaller base of the trapezoid is given as 18 cm, the height is 9 cm, and the acute angle is 45 degrees.

Let's substitute these values into the formula and calculate the area.

Area = (18 + b) * 9 / 2

To find the length of the larger base, we can use the trigonometric relationship between the sides and angles of a right triangle. Since we know the acute angle is 45 degrees, we can use the fact that the sides of an isosceles right triangle are equal.

Let's denote the length of the larger base as b. Then, we can express it in terms of the smaller base using the trigonometric relationship:

b = 18 + 18 * tan(45)

Now, let's substitute this value of b into the formula for the area:

Area = (18 + (18 + 18 * tan(45))) * 9 / 2

To calculate the area, we need to evaluate the expression inside the parentheses and then perform the multiplication and division.

Let's calculate the area using the given values and the formula:

Area = (18 + (18 + 18 * tan(45))) * 9 / 2

Using a calculator, we find that the area of the isosceles trapezoid is approximately 162.36 square centimeters.

Please note that the calculations are based on the given values and the formula for the area of an isosceles trapezoid.