Question

В основании прямой призмы лежит прямоугольный треугольник с катетами 4см и 5 см. Найдите площадь поверхности призмы, если боковое ребро 6 см.​

Answer 1

Ответ:

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Объяснение:

Answer 2

Calculation of the Surface Area of the Prism

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

The prism is based on a right triangle with legs measuring 4 cm and 5 cm. Let's label the legs as a = 4 cm and b = 5 cm.

The lateral face of the prism is a rectangle with dimensions equal to the lengths of the legs of the right triangle. So, the dimensions of the lateral face are 4 cm (width) and 5 cm (height).

The area of the lateral face can be calculated as the product of the width and height:

Area of the lateral face = 4 cm * 5 cm = 20 cm².

The other two faces of the prism are congruent triangles with legs measuring 4 cm, 5 cm, and a hypotenuse equal to the length of the lateral edge, which is 6 cm.

To calculate the area of one of these triangular faces, we can use the formula for the area of a triangle:

Area of a triangle = (base * height) / 2.

In this case, the base of the triangle is 4 cm and the height is 5 cm. Plugging these values into the formula, we get:

Area of one triangular face = (4 cm * 5 cm) / 2 = 10 cm².

Since there are two congruent triangular faces, the total area of both triangular faces is:

Total area of both triangular faces = 2 * 10 cm² = 20 cm².

Finally, to find the total surface area of the prism, we sum up the areas of all its faces:

Total surface area of the prism = Area of the lateral face + Total area of both triangular faces = 20 cm² + 20 cm² = 40 cm².

Therefore, the surface area of the prism is 40 cm².

I hope this helps! Let me know if you have any further questions.