Question
An illustration shows a net version of a triangular prism. The net model shows 3 rectangles top to bottom. Identical triangles are attached to the left and right of the middle rectangle. Parts are labeled with measurements. The top and bottom rectangles have a length measuring 10 centimeters and a width measuring 5 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 4 centimeters. The base of the triangle measures 5 centimeters. The base shares an edge with the middle rectangle.
What is the surface area of the net of the triangular prism?
(1 point)
square centimeters
What is the surface area of the net of the triangular prism?
(1 point)
square centimeters
Answers
GPT-4o mini
To find the surface area of the net of the triangular prism, we need to calculate the area of all the shapes in the net, which includes two triangles and three rectangles.
1. **Area of the triangular bases**: Each triangle has a base (b) of 5 cm and a height (h) of 4 cm.
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \, \text{cm} \times 4 \, \text{cm} = 10 \, \text{cm}^2
\]
Since there are two triangles:
\[
\text{Total area of triangles} = 2 \times 10 \, \text{cm}^2 = 20 \, \text{cm}^2
\]
2. **Area of the rectangles**:
- **Top rectangle**: Length = 10 cm, Width = 5 cm.
\[
\text{Area of top rectangle} = 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2
\]
- **Middle rectangle**: Length = 10 cm, Width = 5 cm (same size as the top rectangle).
\[
\text{Area of middle rectangle} = 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2
\]
- **Bottom rectangle**: Length = 10 cm, Width = 5 cm (same size as the top rectangle).
\[
\text{Area of bottom rectangle} = 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2
\]
Adding up the areas of the three rectangles:
\[
\text{Total area of rectangles} = 50 \, \text{cm}^2 + 50 \, \text{cm}^2 + 50 \, \text{cm}^2 = 150 \, \text{cm}^2
\]
3. **Total surface area of the prism**:
\[
\text{Total surface area} = \text{Total area of triangles} + \text{Total area of rectangles} = 20 \, \text{cm}^2 + 150 \, \text{cm}^2 = 170 \, \text{cm}^2
\]
Thus, the surface area of the net of the triangular prism is **170 square centimeters**.
1. **Area of the triangular bases**: Each triangle has a base (b) of 5 cm and a height (h) of 4 cm.
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \, \text{cm} \times 4 \, \text{cm} = 10 \, \text{cm}^2
\]
Since there are two triangles:
\[
\text{Total area of triangles} = 2 \times 10 \, \text{cm}^2 = 20 \, \text{cm}^2
\]
2. **Area of the rectangles**:
- **Top rectangle**: Length = 10 cm, Width = 5 cm.
\[
\text{Area of top rectangle} = 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2
\]
- **Middle rectangle**: Length = 10 cm, Width = 5 cm (same size as the top rectangle).
\[
\text{Area of middle rectangle} = 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2
\]
- **Bottom rectangle**: Length = 10 cm, Width = 5 cm (same size as the top rectangle).
\[
\text{Area of bottom rectangle} = 10 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2
\]
Adding up the areas of the three rectangles:
\[
\text{Total area of rectangles} = 50 \, \text{cm}^2 + 50 \, \text{cm}^2 + 50 \, \text{cm}^2 = 150 \, \text{cm}^2
\]
3. **Total surface area of the prism**:
\[
\text{Total surface area} = \text{Total area of triangles} + \text{Total area of rectangles} = 20 \, \text{cm}^2 + 150 \, \text{cm}^2 = 170 \, \text{cm}^2
\]
Thus, the surface area of the net of the triangular prism is **170 square centimeters**.