Question

АВСДА1В1С1Д1 - пряма призма, в основі якої лежить прямокутник із сторонами 12см і 4см. Діагональ бічної грані, що містить сторону 12см дорівнює 20 см. Знайти площу повної поверхні призми.

Answer 1

Відповідь:

Покрокове пояснення:

фото

Answer 2

To find the surface area of the prism, we need to calculate the areas of all its faces and then sum them up.

Given information:

- The prism has a rectangular base with sides measuring 12 cm and 4 cm. - The diagonal of one of the lateral faces, which contains the side measuring 12 cm, is 20 cm.

Calculating the surface area:

1. The base of the prism is a rectangle with sides measuring 12 cm and 4 cm. The area of the base is given by the formula: Area = length × width. Therefore, the area of the base is 12 cm × 4 cm = 48 cm².

2. The prism has two identical lateral faces, each of which is a rectangle. The diagonal of one of these rectangles, which contains the side measuring 12 cm, is given as 20 cm. We can use the Pythagorean theorem to find the other side of this rectangle.

Let's denote the other side of the rectangle as 'x'. According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the legs are 4 cm and x cm, and the hypotenuse is 20 cm.

Applying the Pythagorean theorem, we have: 4² + x² = 20² 16 + x² = 400 x² = 400 - 16 x² = 384 x = √384 x ≈ 19.6 cm

Therefore, the other side of the rectangle is approximately 19.6 cm.

The area of each lateral face is given by the formula: Area = length × width. In this case, the length is 12 cm and the width is 19.6 cm. Therefore, the area of each lateral face is approximately 12 cm × 19.6 cm ≈ 235.2 cm².

3. The prism also has two identical triangular faces. The area of each triangular face can be calculated using the formula: Area = (base × height) / 2. In this case, the base is 12 cm and the height is 4 cm. Therefore, the area of each triangular face is (12 cm × 4 cm) / 2 = 24 cm².

4. To find the total surface area of the prism, we sum up the areas of all its faces: Total surface area = 2 × (area of base) + 2 × (area of each lateral face) + 2 × (area of each triangular face) Total surface area = 2 × 48 cm² + 2 × 235.2 cm² + 2 × 24 cm² Total surface area = 96 cm² + 470.4 cm² + 48 cm² Total surface area ≈ 614.4 cm²

Therefore, the approximate total surface area of the prism is 614.4 cm².