use the net to find the surface area prism

8in 15in 17in height9

Net? Is this a triangular right prism? http://www.mathopenref.com/prismarea.html

To find the surface area of a prism, we need to know the dimensions of the bases and the height.

In this case, you mentioned that the prism has a height of 9 inches and the base dimensions are 8 inches and 15 inches.

To calculate the surface area, we need to find the areas of both bases and the lateral surface area.

1. Area of the base:
To find the area of the rectangular base, multiply the length (15 inches) by the width (8 inches):
Area of the base = Length x Width = 15 in x 8 in = 120 square inches.

2. Lateral Surface Area:
The lateral surface area is the sum of the areas of all the rectangular faces that are not the bases.

For a prism, the lateral surface area is equal to the perimeter of the base multiplied by the height.
The perimeter of a rectangle is found by adding the lengths of all sides.

In this case, the perimeter of the base is given by:
Perimeter of the base = 2 x (Length + Width) = 2 x (15 in + 8 in) = 2 x 23 in = 46 in.

Now, multiply the perimeter of the base (46 inches) by the height (9 inches) to get the lateral surface area:
Lateral Surface Area = Perimeter of the base x Height = 46 in x 9 in = 414 square inches.

3. Total Surface Area:
To find the total surface area, add the areas of both bases to the lateral surface area:
Total Surface Area = 2 x Area of the base + Lateral Surface Area
Total Surface Area = 2 x 120 square inches + 414 square inches = 240 square inches + 414 square inches = 654 square inches.

Therefore, the surface area of the prism is 654 square inches.

To find the surface area of a prism, you need to know the lengths of the sides (or bases) and the height of the prism. In this case, the prism has a height of 9 inches and the lengths of the sides are given as 8 inches, 15 inches, and 17 inches.

To calculate the surface area of a prism, you first need to find the area of each face and then add them up.

Here's how you can do it:

1. Identify the two bases of the prism. In this case, the bases are two rectangles with dimensions 8 inches by 15 inches.

2. Calculate the area of each base. The formula for the area of a rectangle is length × width. So, for each base, the area would be 8 inches × 15 inches = 120 square inches.

3. Next, calculate the area of the sides. The side faces of a prism are parallelograms. To find the area of a parallelogram, you multiply the base (in this case, the lengths of the sides) by the height (9 inches). You need to calculate this for each side.

- For the side with lengths 8 inches and 17 inches, calculate: 8 inches × 9 inches = 72 square inches.
- For the opposite side with the same lengths, the area would also be 72 square inches.

4. Lastly, add up the areas of all the faces to find the total surface area of the prism:

Total Surface Area = (2 × Base Area) + (4 × Side Area)
= (2 × 120 square inches) + (4 × 72 square inches)
= 240 square inches + 288 square inches
= 528 square inches

Therefore, the surface area of the given prism is 528 square inches.