Question

СРОООООЧНООООО В прямоугольной трапеции АВСК большая боковая сторона равна 3см, угол К равен 45 градусов , а высота СН делит основание АК пополам. Найдите площадь трапеции

Answer 1

Рассмотрим треугольник СНК. т.к. СН - высота, а угол К=45, то угол КСН=45 (180-(90+45)=45) => треугольник СНК - равнобедренный и НК=СН=1,5 см. Sтреуг=1/2*СН*НК=1/2*1,5*1,5=1,125 кв.см
рассмотрим АВСН. АВСН - параллелограмм, т.к. ВС параллельно АН и АВ параллельно СН. Sпар=1,5*1,5=2,25 кв.см
Sтрап=1,125+2,25=3,375 кв.см

Answer 2

1)Дано:ABCK - трапеция, ∠A = ∠B = 90°,CK=3см, ∠K=45°, CH⊥AK, AH=HK=              Найти:  - ?Решение: = cos ∠KHK = CK·cos ∠K = 3· см∠HCK = 90°-45°=45°, т.е. ΔHCK - равнобедренный ⇒СH = HK = ·CH·(BC + AK) = ·(HK +2HK) = ·HK² =  = см²Ответ: 6,75 см²

Answer 3

Calculation of the Area of a Trapezoid

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

Area = (sum of the lengths of the parallel sides) * (height) / 2

In this case, we are given the following information about the trapezoid ABCD: - The larger parallel side (AB) is 3 cm long. - Angle K is 45 degrees. - The height (CH) divides the base (AK) in half.

Let's calculate the area of the trapezoid step by step.

Step 1: Finding the Length of Side CK

Since the height (CH) divides the base (AK) in half, we can conclude that CK = AK / 2.

Step 2: Finding the Length of Side AK

To find the length of side AK, we can use the trigonometric relationship in a right triangle. In triangle ACH, angle ACH is 45 degrees, and we know that CH = AK / 2. Using the sine function, we have:

sin(45 degrees) = CH / AK

Simplifying the equation, we get:

1 / √2 = CH / AK

Rearranging the equation, we find:

AK = 2CH / √2

Step 3: Calculating the Area

Now that we have the lengths of sides AK and CK, we can calculate the area of the trapezoid using the formula mentioned earlier:

Area = (AB + CK) * CH / 2

Substituting the given values, we have:

Area = (3 + CK) * CH / 2

Substituting CK = AK / 2 and AK = 2CH / √2, we get:

Area = (3 + (2CH / √2)) * CH / 2

Simplifying the equation, we have:

Area = (3CH + 2CH√2) / 2

Therefore, the area of the trapezoid ABCD is (3CH + 2CH√2) / 2 square units.

Please note that we need the value of CH to calculate the exact area of the trapezoid. If you provide the value of CH, I can help you calculate the area.