To calculate the surface area of a right triangular prism, we need to consider the areas of each of its faces.
First, let's calculate the area of the two triangular bases. The formula for the area of a triangle is 1/2 * base * height.
Since the prism is right-angled, the base and height of the triangle are equal to the two sides perpendicular to each other.
Area of a triangle = 1/2 * base * height = 1/2 * 15 ft * 15 ft = 112.5 ft²
The prism has two triangular bases, so the total area of the bases is 2 * 112.5 ft² = 225 ft².
Next, we need to calculate the area of the three rectangular faces. The formula for the area of a rectangle is length * width.
The length of each rectangular face is equal to the height of the prism, which is 15 ft. The width of each face is equal to the side length, which is also 15 ft.
Area of a rectangle = length * width = 15 ft * 15 ft = 225 ft²
The prism has three rectangular faces, so the total area of the rectangular faces is 3 * 225 ft² = 675 ft².
Finally, to find the total surface area of the prism, we add the areas of the bases and the rectangular faces.
Total surface area = area of bases + area of rectangular faces = 225 ft² + 675 ft² = 900 ft²
Therefore, the surface area of the right triangular prism is 900 ft².
Calculate the surface area of a right triangular prism. Each edge length is 15 ft.
3 answers
Wrong
I apologize for the incorrect calculation earlier. Let's calculate the surface area of the right triangular prism correctly.
A right triangular prism has two triangular bases and three rectangular faces.
1. Triangular Base:
The area of a triangle is given by the formula 1/2 * base * height. Since the prism has a right triangle as a base, we need to determine the base and height.
In this case, each edge length is given as 15 ft, so the base and height of the triangle are also 15 ft.
Area of a triangular base = 1/2 * base * height = 1/2 * 15 ft * 15 ft = 112.5 ft²
Since there are two triangular bases, the total area of the bases is 2 * 112.5 ft² = 225 ft².
2. Rectangular Faces:
The length of each rectangular face is equal to the height of the prism, which is 15 ft.
The width of each rectangular face can be determined by considering one side of the triangular base, which is 15 ft.
Area of a rectangular face = length * width = 15 ft * 15 ft = 225 ft²
Since there are three rectangular faces, the total area of the rectangular faces is 3 * 225 ft² = 675 ft².
Total Surface Area = Area of Bases + Area of Rectangular Faces = 225 ft² + 675 ft² = 900 ft²
Therefore, the surface area of the right triangular prism is 900 ft².
A right triangular prism has two triangular bases and three rectangular faces.
1. Triangular Base:
The area of a triangle is given by the formula 1/2 * base * height. Since the prism has a right triangle as a base, we need to determine the base and height.
In this case, each edge length is given as 15 ft, so the base and height of the triangle are also 15 ft.
Area of a triangular base = 1/2 * base * height = 1/2 * 15 ft * 15 ft = 112.5 ft²
Since there are two triangular bases, the total area of the bases is 2 * 112.5 ft² = 225 ft².
2. Rectangular Faces:
The length of each rectangular face is equal to the height of the prism, which is 15 ft.
The width of each rectangular face can be determined by considering one side of the triangular base, which is 15 ft.
Area of a rectangular face = length * width = 15 ft * 15 ft = 225 ft²
Since there are three rectangular faces, the total area of the rectangular faces is 3 * 225 ft² = 675 ft².
Total Surface Area = Area of Bases + Area of Rectangular Faces = 225 ft² + 675 ft² = 900 ft²
Therefore, the surface area of the right triangular prism is 900 ft².