Question

АBCK-прямоугольная трапеция,СК=3корень из 2см СК- боковая сторона,угол К=45град,СН-высота,АН=НК,найти площадь трапеции.

Answer 1

В прямоугольном, равнобедренном ΔСНК с гипотенузой 3√2 и углами <K = <KCH = 45, находим катеты
СН = СК = 3√2 * cos 45 = 3√2 * 2√2 = 12 (cм) = ВС = АН(по условию)
В прямоугольной трапеции с основаниями  ВС = 12 и АК = АН + НК = 24 и высотой СН =12
площадь трапеции равна полусумме оснований * на высоту
S = (BC + AK) : 2 * CН = (12 + 24) : 2 * 12 = 30 (см²)

Answer 2

Problem Analysis

We are given a trapezoid ABCD, where ABCK is a rectangle, SK = 3√2 cm, CK is a lateral side, angle K = 45 degrees, CH is the height, and AN = NK. We need to find the area of the trapezoid.

Solution

To find the area of the trapezoid, we can use the formula: Area = (sum of the lengths of the parallel sides) * (height) / 2.

Let's break down the problem step by step:

1. Find the length of side AB. 2. Find the length of side CD. 3. Find the height CH. 4. Calculate the area of the trapezoid using the formula.

Step 1: Find the length of side AB

We are given that ABCK is a rectangle, and we know that angle K = 45 degrees. In a rectangle, opposite sides are equal in length. Therefore, AB = CK.

Step 2: Find the length of side CD

We don't have direct information about the length of side CD. However, we can use the fact that ABCK is a rectangle to find it indirectly. Since ABCK is a rectangle, opposite sides are parallel and equal in length. Therefore, CD = AB.

Step 3: Find the height CH

We are given that AN = NK. This means that the trapezoid ABCD is an isosceles trapezoid, where the non-parallel sides are equal in length. Therefore, CH = NK.

Step 4: Calculate the area of the trapezoid

Now that we have the lengths of the parallel sides (AB and CD) and the height (CH), we can calculate the area of the trapezoid using the formula: Area = (AB + CD) * CH / 2.

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

Calculation

1. AB = CK = 3√2 cm 2. CD = AB = 3√2 cm 3. CH = NK

Since we don't have the value of NK, we cannot calculate the exact area of the trapezoid without additional information.

Please provide the value of NK or any other missing information so that we can proceed with the calculation.