Question
Find the surface area of this prism.
What is the surface area of this prism? Solve on paper and enter your answer on Zearn. You can use the calculator to help you solve.
L-shaped prism. The base has side lengths labeled 1 cm, 3 cm, 5 cm, 1 cm and 4 cm, with 1 side unlabeled. The height of the prism measures 6 cm.
The surface area of the prism is
cm
2
.
What is the surface area of this prism? Solve on paper and enter your answer on Zearn. You can use the calculator to help you solve.
L-shaped prism. The base has side lengths labeled 1 cm, 3 cm, 5 cm, 1 cm and 4 cm, with 1 side unlabeled. The height of the prism measures 6 cm.
The surface area of the prism is
cm
2
.
Answers
GPT-4o mini
To find the surface area of an L-shaped prism, we start by calculating the area of the base and then find the areas of the lateral surfaces. Here's how we'll do it step by step.
1. **Calculate the area of the base**:
The base is an L-shape formed by two rectangles. To find the area of the L-shaped base, we can break it down into two rectangles.
If we interpret the dimensions given as:
- The longer rectangle with sides 5 cm and 4 cm (extends vertically),
- The smaller rectangle with sides 3 cm and 1 cm (extends horizontally).
Area of the larger rectangle = Length × Width = 5 cm × 4 cm = 20 cm².
Area of the smaller rectangle = Length × Width = 3 cm × 1 cm = 3 cm².
To find the total area of the L-shaped base, we can also note that the area of the inner rectangle formed is subtracted out.
The area of the inner rectangle (cut-out) with dimensions 1 cm and 1 cm = 1 cm².
Therefore, the total area of the base = (20 cm² + 3 cm² - 1 cm²) = 22 cm².
2. **Calculate the surface area of the lateral faces**:
The prism has four lateral faces, corresponding to each side of the base which gets extended up to the height of the prism (6 cm).
- For the base side of 1 cm: Area = 1 cm × 6 cm = 6 cm².
- For the base side of 3 cm: Area = 3 cm × 6 cm = 18 cm².
- For the base side of 5 cm: Area = 5 cm × 6 cm = 30 cm².
- For the base side of 4 cm: Area = 4 cm × 6 cm = 24 cm².
Total area of the lateral faces = 6 cm² + 18 cm² + 30 cm² + 24 cm² = 78 cm².
3. **Calculate total surface area**:
Now, we add the area of the base and the lateral faces:
Total Surface Area = Area of the base + Lateral surface area
Total Surface Area = 22 cm² + 78 cm² = 100 cm².
Thus, the surface area of the prism is **100 cm²**.
1. **Calculate the area of the base**:
The base is an L-shape formed by two rectangles. To find the area of the L-shaped base, we can break it down into two rectangles.
If we interpret the dimensions given as:
- The longer rectangle with sides 5 cm and 4 cm (extends vertically),
- The smaller rectangle with sides 3 cm and 1 cm (extends horizontally).
Area of the larger rectangle = Length × Width = 5 cm × 4 cm = 20 cm².
Area of the smaller rectangle = Length × Width = 3 cm × 1 cm = 3 cm².
To find the total area of the L-shaped base, we can also note that the area of the inner rectangle formed is subtracted out.
The area of the inner rectangle (cut-out) with dimensions 1 cm and 1 cm = 1 cm².
Therefore, the total area of the base = (20 cm² + 3 cm² - 1 cm²) = 22 cm².
2. **Calculate the surface area of the lateral faces**:
The prism has four lateral faces, corresponding to each side of the base which gets extended up to the height of the prism (6 cm).
- For the base side of 1 cm: Area = 1 cm × 6 cm = 6 cm².
- For the base side of 3 cm: Area = 3 cm × 6 cm = 18 cm².
- For the base side of 5 cm: Area = 5 cm × 6 cm = 30 cm².
- For the base side of 4 cm: Area = 4 cm × 6 cm = 24 cm².
Total area of the lateral faces = 6 cm² + 18 cm² + 30 cm² + 24 cm² = 78 cm².
3. **Calculate total surface area**:
Now, we add the area of the base and the lateral faces:
Total Surface Area = Area of the base + Lateral surface area
Total Surface Area = 22 cm² + 78 cm² = 100 cm².
Thus, the surface area of the prism is **100 cm²**.