Question
Base length 12 cm
Base width length 6 cm
Height 4 cm
Sides 5 cm
Find the TOTAL surface area of this triangular prism in cm².
"Hint: Remember, the triangle is always the true base (bottom).
24 cm 2
192 cm 2
202 cm 2
216 cm 2
Base width length 6 cm
Height 4 cm
Sides 5 cm
Find the TOTAL surface area of this triangular prism in cm².
"Hint: Remember, the triangle is always the true base (bottom).
24 cm 2
192 cm 2
202 cm 2
216 cm 2
Answers
GPT-4o mini
To find the total surface area of the triangular prism, we need to calculate the areas of the triangular bases and the rectangular lateral faces.
1. **Area of the triangular base**:
The base of the triangle is given as 12 cm, and the height of the triangle is given as 4 cm.
\[
\text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 \text{ cm} \times 4 \text{ cm} = 24 \text{ cm}^2
\]
Since the prism has two triangular bases, the total area for the triangular bases is:
\[
\text{Total area of triangles} = 2 \times 24 \text{ cm}^2 = 48 \text{ cm}^2
\]
2. **Area of the rectangular lateral faces**:
The prism has three rectangular lateral faces, corresponding to the sides and height of the prism. The sides are given as 5 cm.
- Lateral face 1 (base length * height):
\[
\text{Area} = 12 \text{ cm} \times 4 \text{ cm} = 48 \text{ cm}^2
\]
- Lateral face 2 (base width * height):
\[
\text{Area} = 6 \text{ cm} \times 4 \text{ cm} = 24 \text{ cm}^2
\]
- Lateral face 3 (side length * height):
\[
\text{Area} = 5 \text{ cm} \times 4 \text{ cm} = 20 \text{ cm}^2
\]
Now, we sum up the areas of the three rectangular lateral faces:
\[
\text{Total area of rectangles} = 48 \text{ cm}^2 + 24 \text{ cm}^2 + 20 \text{ cm}^2 = 92 \text{ cm}^2
\]
3. **Total surface area of the prism**:
Finally, we add the area of the triangular bases and the area of the rectangular lateral faces:
\[
\text{Total Surface Area} = \text{Total area of triangles} + \text{Total area of rectangles} = 48 \text{ cm}^2 + 92 \text{ cm}^2 = 140 \text{ cm}^2
\]
Thus, the total surface area of the triangular prism is **140 cm²**. However, the options provided don't include this value. Please verify if any additional details were missed that could affect the calculations, or if there's an error in the data.
1. **Area of the triangular base**:
The base of the triangle is given as 12 cm, and the height of the triangle is given as 4 cm.
\[
\text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 12 \text{ cm} \times 4 \text{ cm} = 24 \text{ cm}^2
\]
Since the prism has two triangular bases, the total area for the triangular bases is:
\[
\text{Total area of triangles} = 2 \times 24 \text{ cm}^2 = 48 \text{ cm}^2
\]
2. **Area of the rectangular lateral faces**:
The prism has three rectangular lateral faces, corresponding to the sides and height of the prism. The sides are given as 5 cm.
- Lateral face 1 (base length * height):
\[
\text{Area} = 12 \text{ cm} \times 4 \text{ cm} = 48 \text{ cm}^2
\]
- Lateral face 2 (base width * height):
\[
\text{Area} = 6 \text{ cm} \times 4 \text{ cm} = 24 \text{ cm}^2
\]
- Lateral face 3 (side length * height):
\[
\text{Area} = 5 \text{ cm} \times 4 \text{ cm} = 20 \text{ cm}^2
\]
Now, we sum up the areas of the three rectangular lateral faces:
\[
\text{Total area of rectangles} = 48 \text{ cm}^2 + 24 \text{ cm}^2 + 20 \text{ cm}^2 = 92 \text{ cm}^2
\]
3. **Total surface area of the prism**:
Finally, we add the area of the triangular bases and the area of the rectangular lateral faces:
\[
\text{Total Surface Area} = \text{Total area of triangles} + \text{Total area of rectangles} = 48 \text{ cm}^2 + 92 \text{ cm}^2 = 140 \text{ cm}^2
\]
Thus, the total surface area of the triangular prism is **140 cm²**. However, the options provided don't include this value. Please verify if any additional details were missed that could affect the calculations, or if there's an error in the data.