Find the surface area of the right prism with the given features: A right triangle with legs of length 12 a base of length 9 and height equals 23.

I assume the prism has a triangular base and a height of 23.

A right triangle with legs of length 12 has sides 12,12,12√2

so, where does the 9 come in?

Do you mean a right triangle with legs of length 9 and 12, and thus a hypotenuse of 15?

If so, then add up the areas of
two triangles, each 1/2 x 9x12
three rectangles with dimensions
9x23, 12x23, 15x23

Yes Steve. Triangular base. She just said leg lengths of 12, a base of 9, and height of 23.

To find the surface area of a right prism, you need to calculate the areas of all its faces and then sum them up.

The given prism has a right triangle as its base with legs of length 12 and a base of length 9. To find the area of this right triangle, you can use the formula: Area = (1/2) * base * height.

In this case, the base of the triangle is 9 and the height is 12. Plugging these values into the formula, we get:

Area = (1/2) * 9 * 12 = 54 square units.

Now, a right prism also has two rectangular faces, one on top and one on the bottom. The length of these rectangular faces is equal to the base of the right triangle, which is 9, and the width is equal to the longer leg of the triangle, which is 12. So the area of each rectangular face is:

Area = length * width = 9 * 12 = 108 square units.

Additionally, a right prism has three rectangular faces as its lateral faces. The length and width of these faces are the same as the corresponding dimensions of the right triangle. So the area of each lateral face is also 108 square units.

Therefore, the surface area of the given right prism is the sum of the areas of all its faces:

Surface Area = Area of triangle + 2 * Area of rectangular face + 3 * Area of lateral face

Surface Area = 54 + 2 * 108 + 3 * 108
Surface Area = 54 + 216 + 324
Surface Area = 594 square units.

Hence, the surface area of the right prism is 594 square units.