To find the surface area of the rectangular prism, we need to calculate the area of each of the 6 rectangles and then add them up.
Area of the first rectangle = 54 square inches
Area of the second rectangle = 24 square inches
Area of the third rectangle = 36 square inches
The fourth rectangle is similar to the second one, so its area is 24 square inches as well.
The fifth and sixth rectangles are on the top and bottom of the prism and are similar to the first rectangle, so each of their areas is 54 square inches.
Now we calculate the total surface area:
Total surface area = (54 + 24 + 36) + (54 + 24 + 54)
Total surface area = 162 + 132
Total surface area = 294 square inches
Therefore, the surface area of the rectangular prism is 294 square inches.
Use the image to answer the question.
An illustration shows the unfolded version of a rectangular prism composed of 6 rectangles. There are four adjoining rectangles positioned horizontally. The first and third are similar and bigger. The second and fourth are similar and smaller. The area of the second rectangle is labeled 24 square inches. The third rectangle shares the top and bottom sides with two similar rectangles, one on each side. The area of the top rectangle is labeled as 54 square inches and the area of the third rectangle is labeled as 36 square inches.
What is the surface area of the rectangular prism?
in.2
7 answers
Use the image to answer the question.
An illustration shows the unfolded version of a prism comprising of 2 triangles and 3 rectangles. Dimensions are marked. There are three adjoining rectangles positioned horizontally. The first and third rectangles appear identical. The second rectangle in the middle is smaller and is labeled as 3 inches in length and 2 inches in width. The center rectangle shares its top and bottom sides with the bases of identical triangles. A side of the bottom triangle is labeled 6 inches. The top side of the third rectangle on the right is marked as a line connecting point upper A on the upper right vertex and point upper B on the upper left vertex. All the common sides are shown as dashed lines.
What is the length of AB ?
in.
An illustration shows the unfolded version of a prism comprising of 2 triangles and 3 rectangles. Dimensions are marked. There are three adjoining rectangles positioned horizontally. The first and third rectangles appear identical. The second rectangle in the middle is smaller and is labeled as 3 inches in length and 2 inches in width. The center rectangle shares its top and bottom sides with the bases of identical triangles. A side of the bottom triangle is labeled 6 inches. The top side of the third rectangle on the right is marked as a line connecting point upper A on the upper right vertex and point upper B on the upper left vertex. All the common sides are shown as dashed lines.
What is the length of AB ?
in.
Given that the sides of the bottom triangle are 6 inches and this triangle is similar to the top triangle, we can set up a proportion to find the length of AB.
Let the length of AB be x inches. Since the sides of the bottom triangle are in the ratio 6:x, we can set up the following proportion:
6 / x = 6 / 6
Cross multiply to solve for x:
6 * 6 = x
36 = x
Therefore, the length of AB is 36 inches.
Let the length of AB be x inches. Since the sides of the bottom triangle are in the ratio 6:x, we can set up the following proportion:
6 / x = 6 / 6
Cross multiply to solve for x:
6 * 6 = x
36 = x
Therefore, the length of AB is 36 inches.
Jillian draws a net for a rectangular prism. One face of the prism has an area of 6 in.2 . A second face has an area of 12 in.2 , and a third face has an area of 9 in.2 . What is the total surface area of Jillian’s prism?
1. 27 in.2
2. 54 in.2
3. 648 in.2
4. 81 in.2
1. 27 in.2
2. 54 in.2
3. 648 in.2
4. 81 in.2
To find the total surface area of the rectangular prism, we need to add up the areas of all the faces.
Given that:
- One face has an area of 6 in^2
- A second face has an area of 12 in^2
- A third face has an area of 9 in^2
Let's calculate the total surface area:
Total surface area = 6 + 12 + 9 + 6 + 12 + 9
Total surface area = 54 in^2
Therefore, the total surface area of Jillian's prism is 54 in^2. The correct answer is option 2: 54 in^2.
Given that:
- One face has an area of 6 in^2
- A second face has an area of 12 in^2
- A third face has an area of 9 in^2
Let's calculate the total surface area:
Total surface area = 6 + 12 + 9 + 6 + 12 + 9
Total surface area = 54 in^2
Therefore, the total surface area of Jillian's prism is 54 in^2. The correct answer is option 2: 54 in^2.
A rectangular prism has length of 2 feet, a width of 3 feet, and a height of 4 feet. What is the surface area of the rectangular prism? Draw a net to help you find your answer.
? square feet
? square feet
To find the surface area of a rectangular prism, we calculate the area of each face and then sum them up.
Given:
Length = 2 feet
Width = 3 feet
Height = 4 feet
First, let's draw a net of the rectangular prism:
The net consists of 6 faces: 2 rectangles for the top and bottom, and 4 rectangles for the sides.
Calculation of surface area:
1. Top and Bottom Faces:
Area = Length * Width
Area = 2 * 3 = 6 sq ft (for each face)
2. Side Faces (4):
Area = Length * Height
Area = 2 * 4 = 8 sq ft (for each face)
Now, to find the total surface area:
Total Surface Area = 2(6) + 4(8)
Total Surface Area = 12 + 32
Total Surface Area = 44 square feet
Therefore, the surface area of the rectangular prism is 44 square feet.
Given:
Length = 2 feet
Width = 3 feet
Height = 4 feet
First, let's draw a net of the rectangular prism:
The net consists of 6 faces: 2 rectangles for the top and bottom, and 4 rectangles for the sides.
Calculation of surface area:
1. Top and Bottom Faces:
Area = Length * Width
Area = 2 * 3 = 6 sq ft (for each face)
2. Side Faces (4):
Area = Length * Height
Area = 2 * 4 = 8 sq ft (for each face)
Now, to find the total surface area:
Total Surface Area = 2(6) + 4(8)
Total Surface Area = 12 + 32
Total Surface Area = 44 square feet
Therefore, the surface area of the rectangular prism is 44 square feet.