Question

в основании прямой призмы лежит ромбсо стороной 5см и диагональю 6см. боковое ребро призмы равно 3см найти площадь полной поверхности и ее меньшую диагональ.

Answer 1

ну я тут посчитал и как бы у ромба получается 2 диагонали одна 6 и 8 видими 6 это меньшее, а 8 большее, и площадь пп призмы вычисляется как Sпп=P*j+2Sосн.=60+48=108

 

Answer 2

Given Information:

- The base of the prism is a rhombus with a side length of 5 cm and a diagonal of 6 cm. - The lateral edge of the prism is 3 cm.

Finding the Surface Area of the Prism:

To find the surface area of the prism, we need to calculate the area of each face and then sum them up.

1. The area of the base: - The base of the prism is a rhombus. - The formula to calculate the area of a rhombus is A = (d1 * d2) / 2, where d1 and d2 are the diagonals of the rhombus. - In this case, the diagonals are given as 5 cm and 6 cm. - Plugging in the values, we get A = (5 * 6) / 2 = 15 cm^2.

2. The area of the lateral faces: - The lateral faces of the prism are rectangles. - The formula to calculate the area of a rectangle is A = length * width. - In this case, the length is the lateral edge of the prism, which is given as 3 cm. - The width is the same as the side length of the base rhombus, which is 5 cm. - Plugging in the values, we get A = 3 * 5 = 15 cm^2 for each lateral face. - Since there are four lateral faces, the total area of the lateral faces is 4 * 15 = 60 cm^2.

3. The total surface area: - To find the total surface area, we need to sum up the areas of the base and the lateral faces. - The total surface area is 15 cm^2 (base) + 60 cm^2 (lateral faces) = 75 cm^2.

Finding the Smaller Diagonal:

To find the smaller diagonal of the base rhombus, we can use the Pythagorean theorem.

1. Let's denote the smaller diagonal as d. 2. We know that the side length of the rhombus is 5 cm and the larger diagonal is 6 cm. 3. The formula for the smaller diagonal can be derived from the Pythagorean theorem: d^2 = (larger diagonal^2 - side length^2) / 4. 4. Plugging in the values, we get d^2 = (6^2 - 5^2) / 4 = 11 / 4. 5. Taking the square root of both sides, we find d = sqrt(11/4) = sqrt(11) / 2.

Therefore, the smaller diagonal of the base rhombus is sqrt(11) / 2 cm.

Summary:

- The surface area of the prism is 75 cm^2. - The smaller diagonal of the base