Right trapezoid prism has 6400 cm^2 surface area and 46080 cm^3 volume.
The image shows a right trapezoidal prism. A right trapezoidal prism is a three-dimensional solid that has two trapezoidal bases at the bottom and top, and four rectangular lateral faces. The bases are parallel and congruent, and the lateral faces are perpendicular to the bases.
In the image, the base of the prism is a square, and the slope is a triangle. The height of the prism is the distance between the two bases.
The formulas for the surface area and volume of a right trapezoidal prism are as follows:
Surface area = 2(area of base) + (perimeter of base)(height)
Volume = 1/2(sum of bases)(height)
To calculate the surface area and volume of the prism in the image, we need to know the dimensions of the square base and the triangle slope. From the image, we can see that the length of the base of the square is 40 cm, and the height of the triangle is 48 cm. The length of the hypotenuse of the triangle is equal to the slant height of the prism, which is also 48 cm.
To calculate the area of the square base, we simply multiply the length by the width, which is 40 cm * 40 cm = 1600 cm^2.
To calculate the perimeter of the square base, we add up the lengths of all four sides, which is 4 * 40 cm = 160 cm.
Now we can calculate the surface area of the prism:
Surface area = 2(area of base) + (perimeter of base)(height)
Surface area = 2(1600 cm^2) + (160 cm)(48 cm)
Surface area = 6400 cm^2
To calculate the volume of the prism, we need to know the sum of the bases. The sum of the bases is equal to the area of the square base plus the area of the triangle slope. The area of the triangle slope is 1/2 base height, which is 1/2 * 40 cm * 18 cm = 360 cm^2. Therefore, the sum of the bases is 1600 cm^2 + 360 cm^2 = 1960 cm^2.
Now we can calculate the volume of the prism:
Volume = 1/2(sum of bases)(height)
Volume = 1/2(1960 cm^2)(48 cm)
Volume = 46080 cm^3
Therefore, the surface area of the right trapezoidal prism in the image is 6400 cm^2, and the volume is 46080 cm^3.
In addition to the above, here are some other interesting facts about right trapezoidal prisms:
Right trapezoidal prisms are often used in real-world applications, such as in the design of buildings, bridges, and other structures.
Right trapezoidal prisms can be dissected into other geometric shapes, such as cubes, pyramids, and prisms.
The surface area and volume of a right trapezoidal prism can be calculated using relatively simple formulas.
I hope this information is helpful. Please let me know if you have any other questions.