Me find the area of the triangular prism. and show the work

36 in²

Step-by-step explanation:

You can calculate the area of this right prism by adding the area of its faces.

You can observe that the faces of the right prism are:  Three different rectangles and two equal triangles.

The formula for calculate the  area of a rectangle is:

 Where "l" is the lenght and "w" is the width.

The formula for calculate the  area of a triangle is:

Where "b" is the base and "h" is the height.

 You can observe that the hypotenuse of the each triangle is the length of the larger rectangle, then , you can find its value with the Pythagorean Theorem:

Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.

Then, this is:

Therefore, you can add the areas of the faces to find the area of the right prism (Since the triangles are equal, you can multiply the area of one of them by 2). This is:

15: 24

62.5%

step-by-step explanation: