Question

Площадь основания прямоугольной призмы равны 20кв дм. Её боковое ребро равно 7дм. Определи объём призмы.

Answer 1

Объём прямоугольной призмы равен произведению площади на высоту призмы.
20 * 7 = 140 (дм³) - объём призмы.
Ответ: 140 дм³.

Answer 2

Calculation of the Volume of a Rectangular Prism

To find the volume of a rectangular prism, we need to multiply the area of the base by the height of the prism. In this case, we are given the area of the base and the length of one of the lateral edges. Let's calculate the volume.

Given: - Area of the base = 20 square decimeters - Length of one of the lateral edges = 7 decimeters

To calculate the volume, we need to find the height of the prism. Since the base of the prism is a rectangle, we can use the formula for the area of a rectangle to find the height.

The formula for the area of a rectangle is:

Area = length × width

In this case, the area of the base is given as 20 square decimeters. Let's assume the length of the base is L and the width is W. We can set up the following equation:

L × W = 20

Since the base of the prism is a rectangle, the length and width are perpendicular to each other. Therefore, we can rewrite the equation as:

L × W = 20 → L = 20 / W

Now, we are given that one of the lateral edges has a length of 7 decimeters. Let's assume the length of the base is L and the width is W. We can set up the following equation:

2L + 2W + 7 = Perimeter of the base

Since the base of the prism is a rectangle, the length and width are perpendicular to each other. Therefore, we can rewrite the equation as:

2L + 2W + 7 = Perimeter of the base → 2L + 2W = Perimeter of the base - 7

Now, we can substitute the value of L from the first equation into the second equation:

2(20 / W) + 2W = Perimeter of the base - 7

Simplifying the equation:

40 / W + 2W = Perimeter of the base - 7

To find the value of W, we can solve this equation. However, without the exact value of the perimeter of the base, we cannot determine the exact values of L and W. Therefore, we cannot calculate the volume of the prism.

Please provide the exact value of the perimeter of the base so that we can proceed with the calculation.