Find the surface area of the solid.

A right triangular prism with base edges of lengths 6, 8, and 10 and height 2

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The surface area of the prism is the sum of all its surfaces.

The top and bottom have the same shape, namely a right triangle with sides 6,8 and 10. So that should not cause difficulties since the base and height of these two triangles are 6 and 8 respectively.
There are three vertical faces each of height 2 and width equal to the side length (6,8,10) of the base triangle. So the area of these three rectangular faces must be added to complete the area calculation.
Post your work if you are not sure of the answer.

To find the surface area of a right triangular prism, we need to calculate the sum of the areas of its lateral faces and the areas of its two triangular bases.

Step 1: Calculate the area of one triangular base.
The area of a triangle can be calculated using the formula: A = (1/2) * base * height.

Using the given dimensions, the base of the triangle is 6 units and the height is 8 units.
A = (1/2) * 6 * 8
A = 24 square units.

Step 2: Calculate the area of the two triangular bases.
Since there are two triangular bases, we simply double the area of one base.
Total area of the two triangular bases = 2 * 24 = 48 square units.

Step 3: Calculate the area of the lateral faces.
The perimeter of the base triangle is given by the sum of the three base edges.
Perimeter = 6 + 8 + 10 = 24 units.

The height of the prism is given as 2 units.

The lateral faces of the prism are three rectangles, with lengths equal to the perimeter and heights equal to the height of the prism.
Area of the lateral faces = perimeter * height = 24 * 2 = 48 square units.

Step 4: Calculate the total surface area.
Total surface area = Area of the two triangular bases + Area of the lateral faces
Total surface area = 48 + 48 = 96 square units.

Therefore, the surface area of the given solid, a right triangular prism with base edges of lengths 6, 8, and 10 and height 2, is 96 square units.

To find the surface area of a right triangular prism, we need to calculate the areas of all its faces and then add them together.

A right triangular prism has three rectangular faces and two triangular faces.

1. The two triangular faces have base and height given by the dimensions of the right triangle used to form the prism's bases. In this case, the base edges are 6, 8, and 10, and the height is 2.
One triangular face has a base of 6 and a height of 2. So the area of this face is (1/2) * base * height = (1/2) * 6 * 2 = 6.
The other triangular face has a base of 8 and a height of 2. So the area of this face is also 6.

2. The three rectangular faces have lengths corresponding to the length of the base edges and a width corresponding to the height of the prism.
The first rectangular face has dimensions 6 by 2, so its area is 6 * 2 = 12.
The second rectangular face has dimensions 8 by 2, so its area is 8 * 2 = 16.
The third rectangular face has dimensions 10 by 2, so its area is 10 * 2 = 20.

To find the total surface area, we add up the areas of all the faces: 6 + 6 + 12 + 16 + 20 = 60.

Therefore, the surface area of the right triangular prism is 60 square units.