Question

На рисунке изображена пирамида mabcd боковые грани которого - равнобедренные треугольники с боковыми сторонами по 7 см а основание квадрат со сторонами 8 см. чему равна сумма длин всех рёбер пирамиды

Answer 1

60 см.  т. к.         7*4+ 8*4.

Answer 2

Calculation of the Sum of the Lengths of All Edges of the Pyramid

To calculate the sum of the lengths of all edges of the pyramid, we need to determine the lengths of the edges.

The pyramid is depicted as "mABCD" in the diagram, with its lateral faces being isosceles triangles and the base being a square. The lateral sides of the triangles have a length of 7 cm, and the base of the pyramid is a square with sides measuring 8 cm.

To find the lengths of the edges, we can analyze the diagram and use the given information.

Let's break down the calculation step by step:

1. The base of the pyramid is a square with sides measuring 8 cm. Therefore, each side of the square is 8 cm long.

2. The lateral faces of the pyramid are isosceles triangles with sides measuring 7 cm. Since the base of the pyramid is a square, the height of each triangle is equal to the side length of the square, which is 8 cm.

3. To find the length of the slant height of each triangle, we can use the Pythagorean theorem. The slant height (l) can be calculated using the formula: l = √(h^2 + (s/2)^2), where h is the height of the triangle and s is the length of the base of the triangle.

Plugging in the values, we get: l = √(8^2 + (7/2)^2) = √(64 + 24.5) ≈ √88.5 ≈ 9.4 cm.

4. Each triangle has three edges: the base (7 cm), the slant height (9.4 cm), and the other side (7 cm). Therefore, the total length of the edges of each triangle is 7 + 9.4 + 7 = 23.4 cm.

5. Since there are four triangles in the pyramid, we multiply the length of the edges of each triangle by 4 to get the total length of the edges of all the triangles: 23.4 cm * 4 = 93.6 cm.

6. Additionally, we need to consider the edges of the base square. The base square has four edges, each measuring 8 cm. Therefore, the total length of the edges of the base square is 8 cm * 4 = 32 cm.

7. Finally, we add the lengths of the edges of the triangles and the base square to get the sum of the lengths of all the edges of the pyramid: 93.6 cm + 32 cm = 125.6 cm.

Therefore, the sum of the lengths of all the edges of the pyramid is 125.6 cm.