Question

Менша діагональ прямокутної трапеції, довжина якої 12√2 см, с бісектрисою прямого кута. Обчислити площу трапеції, якщо різниця її основ дорівнює 9 см. ( відповідь 198см²) потрібно пояснення ​

Answer 1

Відповідь: 198 см²

Пояснення:

розв'язання завдання додаю

Answer 2

To find the area of a 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, we are given that the smaller diagonal of the trapezoid is 12√2 cm and the difference between the lengths of its bases is 9 cm.

Let's break down the problem step by step:

Step 1: Finding the lengths of the bases

We are given that the difference between the lengths of the bases is 9 cm. Let's assume that the length of the longer base is x cm. Therefore, the length of the shorter base would be x - 9 cm.

Step 2: Finding the height of the trapezoid

We are told that the trapezoid has a bisector of a right angle. This means that the height of the trapezoid is equal to the length of the shorter base, which is x - 9 cm.

Step 3: Calculating the area

Now that we have the lengths of the bases and the height, we can substitute these values into the formula to find the area of the trapezoid:

Area = (a + b) * h / 2 = (x + (x - 9)) * (x - 9) / 2 = (2x - 9) * (x - 9) / 2

To find the value of x, we can use the fact that the smaller diagonal of the trapezoid is 12√2 cm. The smaller diagonal of a trapezoid can be calculated using the formula:

d = √(a^2 + b^2)

where d is the length of the smaller diagonal, and a and b are the lengths of the bases. In this case, we know that d = 12√2 cm, and a = x cm and b = x - 9 cm.

Substituting these values into the formula, we get:

12√2 = √(x^2 + (x - 9)^2)

Squaring both sides of the equation, we get:

288 = x^2 + (x - 9)^2

Expanding and simplifying the equation, we get:

288 = x^2 + x^2 - 18x + 81

Combining like terms, we get:

2x^2 - 18x - 207 = 0

Now we can solve this quadratic equation to find the value of x.