The bases of a right prism are parallelograms with sides a=10 cm, b=6 cm, and altitude of the parallelogram towards side a, ha = 3 cm. Find the surface area of the parallelogram, if the height of the prism is h=12 cm.

The answer is 444cm^2

To find the surface area of the parallelogram, we need to find the sum of the areas of its two bases and the area of its four lateral faces.

1. Area of the base:
The base of the parallelogram is a parallelogram itself, so its area can be calculated using the formula: Area = base x height.
In this case, the base of the parallelogram is side a, which has a length of 10 cm, and the height is ha = 3 cm.
So, the area of the base of the parallelogram is: Area = 10 cm x 3 cm = 30 cm².

2. Area of the top:
The top base of the prism is identical to the bottom base, so its area is also 30 cm².

3. Area of the lateral faces:
The lateral faces of the prism are all rectangles, with one side being the height of the prism (h) and the other side being the length of side b.
The area of a rectangle is given by the formula: Area = length x width.
In this case, the length is 12 cm (height of the prism) and the width is 6 cm (side b).
So, the area of each lateral face of the prism is: Area = 12 cm x 6 cm = 72 cm².

Since there are four lateral faces, the total area of the lateral faces is: 4 x 72 cm² = 288 cm².

4. Total surface area:
The total surface area of the parallelogram is the sum of the areas of the two bases and the four lateral faces.
So, the surface area of the parallelogram is: (2 x 30 cm²) + 288 cm² = 60 cm² + 288 cm² = 348 cm².

Therefore, the surface area of the parallelogram is 348 cm².

To find the surface area of the parallelogram, we need to first calculate the area of each base, and then add the areas of the two bases.

The area of a parallelogram can be calculated using the formula: A = base x height.

In this case, the base of the parallelogram is side a, which is 10 cm, and the height is ha, which is 3 cm.

Therefore, the area of each base is A_base = 10 cm x 3 cm = 30 cm^2.

Since we have two bases in a right prism, the total surface area of the parallelogram is given by:

Surface Area = 2 x A_base = 2 x 30 cm^2 = 60 cm^2.

Therefore, the surface area of the parallelogram is 60 cm^2.

two bases 10*3

two sides 12*10
two sides 12*6