calculate the surface area of each prism.

length 9cm
width 4cm
hieght 8cm

Vanessa,

the answer should be 288cm. for the surface area all you do is multiply lenght width and height

Length * Width * Height = Volume rather than surface area.

What shape is the prism?

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

Given:
Length = 9 cm
Width = 4 cm
Height = 8 cm

Step 1: Finding the areas of each face

- Top and bottom faces (rectangles) have the same dimensions: Length x Width = 9 cm x 4 cm = 36 square cm each.
- Front and back faces (rectangles) also have the same dimensions: Length x Height = 9 cm x 8 cm = 72 square cm each.
- Left and right faces (rectangles) have the same dimensions: Width x Height = 4 cm x 8 cm = 32 square cm each.

Step 2: Adding up the areas

- Total surface area = 2(Top + Bottom) + 2(Front + Back) + 2(Left + Right)
= 2(36 cm²) + 2(72 cm²) + 2(32 cm²)
= 72 cm² + 144 cm² + 64 cm²
= 280 cm²

Therefore, the surface area of the given rectangular prism is 280 square cm.

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

A prism has two identical parallel bases and rectangular sides connecting these bases. In this case, the bases are rectangles and the sides are also rectangles.

The surface area of a prism with rectangular bases can be calculated using the formula:

Surface Area = 2(Area of the Base) + (Perimeter of the Base) × (Height)

Given:
Length = 9 cm
Width = 4 cm
Height = 8 cm

First, we need to find the area of the base. The base is a rectangle, so we can use the formula for the area of a rectangle:

Area of the Base = Length × Width

Area of the Base = 9 cm × 4 cm
Area of the Base = 36 cm²

Next, we need to find the perimeter of the base. Since the base is a rectangle, the perimeter can be calculated using the formula:

Perimeter of the Base = 2(Length + Width)

Perimeter of the Base = 2(9 cm + 4 cm)
Perimeter of the Base = 2(13 cm)
Perimeter of the Base = 26 cm

Now, we can calculate the surface area of the prism using the formula mentioned earlier:

Surface Area = 2(Area of the Base) + (Perimeter of the Base) × (Height)

Surface Area = 2(36 cm²) + (26 cm) × (8 cm)
Surface Area = 72 cm² + 208 cm²
Surface Area = 280 cm²

Therefore, the surface area of the given prism is 280 cm².