the base of a right triangular prism has a width of 8 inches and a height of 6 inches. the length of the third side of the triangle is 10 inches and the length of the prism is 12 inches. What is the surface area of this prism?
I see a surface area of the prism to be made up of 2 triangles and 3 rectangles
Hypotenuse of triangle is 10 (double the 3,4,5 triangle, it was actually given even though it could have been found)
So area = 2(1/2)(6)(8) + 10(6) + 10(8) + 10(10) = 288 inches^2
Omg 2011? wow
Well, well, well, it looks like we have some triangular prism business here! Let's get cracking!
First, we need to calculate the area of the base triangle. The width is 8 inches, and the height is 6 inches, so the formula for the area of a triangle, which is 1/2 times base times height, gives us 1/2 * 8 * 6 = 24 square inches for the base area.
Now, let's calculate the area of the two triangular sides of the prism. Each triangular side has a base length of 8 inches and a height of 6 inches. The formula for the area of a triangle applies here too, so we get 1/2 * 8 * 6 = 24 square inches for each triangular side. Since there are two sides, we multiply that by 2 to get 48 square inches for both sides.
Finally, we need to calculate the area of the two rectangular sides. Both sides have a length of 12 inches and a height of 10 inches. Multiply those two numbers together, and we get 120 square inches for each rectangular side. Multiply that by 2, and we have 240 square inches for both sides.
To find the total surface area, we add up the areas of the base, the two triangular sides, and the two rectangular sides. So 24 + 48 + 240 + 240 = 552 square inches.
So, the surface area of this prism is 552 square inches. Ta-da!
To find the surface area of the right triangular prism, we need to find the area of each face and then sum them up.
First, let's find the area of the base. Since the base is a right triangle, we can use the formula for the area of a triangle, which is 1/2 multiplied by the base multiplied by the height. In this case, the base is 8 inches and the height is 6 inches. Therefore, the area of the base is (1/2) * 8 * 6 = 24 square inches.
Next, let's find the areas of the lateral faces. There are three lateral faces of a prism, and in this case, they are all rectangles. To find the area of a rectangle, we multiply the length by the width. The length of each lateral face is 12 inches, and the width is the same as the length of the third side of the triangle, which is 10 inches. Therefore, the area of each lateral face is 12 * 10 = 120 square inches.
Now, let's find the area of the two triangular faces. Since they are congruent triangles, we can use the same formula as before, which is 1/2 multiplied by the base multiplied by the height. The base of each triangle is 8 inches, and the height is 6 inches. Therefore, the area of each triangular face is (1/2) * 8 * 6 = 24 square inches.
To find the total surface area, we add up the areas of all the faces. Since there is one base, two triangular faces, and three lateral faces, the total surface area is 24 + 24 + 120 + 120 + 120 = 408 square inches.
So, the surface area of this prism is 408 square inches.