To find the surface area of a triangular prism, we need to calculate the area of each individual face and then add them together.
First, we need to find the area of the triangular bases. The base of the triangular prism is a triangle with a base of 8 cm and a height of 6 cm. To find the area of the triangle, we use the formula:
Area = 1/2 * base * height
Area = 1/2 * 8 cm * 6 cm
Area = 24 cm^2
Since there are two triangular bases, the total area of the bases is 2 * 24 cm^2 = 48 cm^2
Next, we need to find the three rectangular faces of the prism. Two of the faces have dimensions of 8 cm by 6 cm, and the third face has dimensions of 6.9 cm by 6 cm.
The total area of the three rectangular faces is:
2 * (8 cm * 6 cm) + 6.9 cm * 6 cm
= 2 * 48 cm^2 + 41.4 cm^2
= 96 cm^2 + 41.4 cm^2
= 137.4 cm^2
Finally, we add the area of the bases and the area of the three rectangular faces to find the total surface area of the triangular prism:
48 cm^2 (bases) + 137.4 cm^2 (rectangular faces)
= 185.4 cm^2
Therefore, the surface area of the triangular prism is approximately 185.4 cm^2 (rounded to the nearest tenth).
Use the image to answer the question.
The image is a diagram showing various shapes and sizes with measurements given. It includes lines and plots with measurements such as 8 cm, 6.9 cm, and 6 cm.
What is the surface area of the triangular prism? Round the answer to the nearest tenth.
(1 point)
cm2
3 answers
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Given the measurements in the image, the triangular prism has a triangular base with a base of 8 cm, a height of 6 cm, and a length of 6.9 cm.
To find the surface area of the triangular prism, we need to calculate the area of each face and then sum them up.
1. The area of each triangular base:
Area = 1/2 * base * height
Area = 1/2 * 8 cm * 6 cm
Area = 24 cm^2
Since there are two triangular bases, the total area for the bases is 2 * 24 cm^2 = 48 cm^2.
2. The three rectangular faces:
- Two faces have dimensions 8 cm by 6.9 cm.
- One face has dimensions 6.9 cm by 6 cm.
The total area of the three rectangular faces will be:
2 * (8 cm * 6.9 cm) + 6.9 cm * 6 cm
= 2 * 55.2 cm^2 + 41.4 cm^2
= 110.4 cm^2 + 41.4 cm^2
= 151.8 cm^2
Adding the area of the bases and the area of the three rectangular faces, we get:
48 cm^2 (bases) + 151.8 cm^2 (rectangular faces)
= 199.8 cm^2
Therefore, the correct surface area of the triangular prism is approximately 199.8 cm^2 (rounded to the nearest tenth).
Given the measurements in the image, the triangular prism has a triangular base with a base of 8 cm, a height of 6 cm, and a length of 6.9 cm.
To find the surface area of the triangular prism, we need to calculate the area of each face and then sum them up.
1. The area of each triangular base:
Area = 1/2 * base * height
Area = 1/2 * 8 cm * 6 cm
Area = 24 cm^2
Since there are two triangular bases, the total area for the bases is 2 * 24 cm^2 = 48 cm^2.
2. The three rectangular faces:
- Two faces have dimensions 8 cm by 6.9 cm.
- One face has dimensions 6.9 cm by 6 cm.
The total area of the three rectangular faces will be:
2 * (8 cm * 6.9 cm) + 6.9 cm * 6 cm
= 2 * 55.2 cm^2 + 41.4 cm^2
= 110.4 cm^2 + 41.4 cm^2
= 151.8 cm^2
Adding the area of the bases and the area of the three rectangular faces, we get:
48 cm^2 (bases) + 151.8 cm^2 (rectangular faces)
= 199.8 cm^2
Therefore, the correct surface area of the triangular prism is approximately 199.8 cm^2 (rounded to the nearest tenth).
7 answers