a right triangular prism has a length of 11 units.Its right triangle face has legs of 3 and 4 and a hypotenuse of 5. what is the surface area of the right triangular prism.

To find the surface area of a right triangular prism, we need to calculate the area of each face and add them up.

1. Area of the right triangle face:
The area of a triangle is given by the formula: (base × height) / 2. In this case, the base is 3 units and the height is 4 units. Therefore, the area of the right triangle face is:
Area = (3 × 4) / 2 = 12 / 2 = 6 square units.

2. Area of the rectangular face:
The rectangular face is a rectangle with dimensions equal to the length of the prism (11 units) and the hypotenuse of the right triangle face (5 units). Therefore, the area of the rectangular face is:
Area = (11 × 5) = 55 square units.

3. Area of the second right triangle face:
The second right triangle face has the same dimensions as the first right triangle face. So, its area is also 6 square units.

Now, let's calculate the surface area by adding up the areas of all the faces:
Total Surface Area = 2 × Area of the right triangle face + Area of the rectangular face
Total Surface Area = 2 × 6 + 55
Total Surface Area = 12 + 55
Total Surface Area = 67 square units.

Therefore, the surface area of the right triangular prism is 67 square units.

To find the surface area of the right triangular prism, we need to calculate the area of each face and then add them all together.

First, let's find the area of the rectangular faces. The rectangular faces are perpendicular to the triangular face.

The length of the prism is given as 11 units, and the height of the prism can be found by using the Pythagorean theorem on the right triangle:

a^2 + b^2 = c^2

3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25

Therefore, the height of the prism is 5 units.

The area of each rectangular face is the product of the length and height:

Area of each rectangular face = length × height = 11 units × 5 units = 55 square units

Since there are two rectangular faces, we have a total of 2 × 55 = 110 square units for the rectangular faces.

Next, let's find the area of the triangular face. The formula for the area of a triangle is:

Area of a triangle = 1/2 × base × height

In this case, the base of the triangle is one of the legs, which is 3 units, and the height of the triangle is the other leg, which is 4 units.

Therefore, the area of the triangular face is:

Area of the triangular face = 1/2 × 3 units × 4 units = 6 square units

Now we can find the total surface area by adding the areas of all the faces:

Total surface area = 110 square units (rectangular faces) + 6 square units (triangular face) = 116 square units

Hence, the surface area of the right triangular prism is 116 square units.