Question

Меньшее основание равнобедренной трапеции равно 8 см боковая сторона 10 см острый угол равно 45 Найти периметр

Answer 1

Решение на фото -----------------------------------------

Answer 2

Given Information

We are given the following information about a trapezoid: - The shorter base of the isosceles trapezoid is 8 cm. - One of the legs (or sides) of the trapezoid is 10 cm. - One of the acute angles of the trapezoid is 45 degrees.

Solution

To find the perimeter of the trapezoid, we need to determine the lengths of the other two sides.

Let's denote the shorter base of the trapezoid as AB (with length 8 cm), and the longer base as CD. We also have one of the legs as BC (with length 10 cm).

Since the trapezoid is isosceles, the angles opposite the bases are congruent. Therefore, angle BCD is also 45 degrees.

To find the length of the longer base CD, we can use the tangent of the angle BCD. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side.

Using the tangent of 45 degrees, we have:

tan(45) = CD / BC

Since the length of BC is 10 cm, we can solve for CD:

CD = tan(45) * BC

Substituting the values, we get:

CD = tan(45) * 10

Using a calculator, we find that tan(45) = 1. Therefore:

CD = 1 * 10 = 10 cm

Now we have the lengths of both bases of the trapezoid: AB = 8 cm and CD = 10 cm.

To find the perimeter of the trapezoid, we add up the lengths of all four sides:

Perimeter = AB + BC + CD + DA

Since the trapezoid is isosceles, the non-parallel sides are congruent. Therefore, BC = DA.

Substituting the values, we get:

Perimeter = 8 + 10 + 10 + BC

To find the length of BC, we can use the Pythagorean theorem. In a right triangle with legs of length 10 cm and 8 cm, the hypotenuse (which is BC) can be found using the formula:

BC = sqrt(10^2 + 8^2)

Using a calculator, we find that BC ≈ 12.81 cm.

Substituting this value into the perimeter formula, we get:

Perimeter = 8 + 10 + 10 + 12.81

Calculating the sum, we find that the perimeter of the trapezoid is approximately 40.81 cm.

Therefore, the perimeter of the trapezoid is approximately 40.81 cm.

Answer

The perimeter of the given trapezoid is approximately 40.81 cm.