A triangular prism. Parts are labeled with measurements. The left side of the triangle measures 8 centimeters. The left side meets the base to form a right angle. The base of the triangle measures 6 centimeters. The hypotenuse side of the triangle measures 10 centimeters. The width of the rectangular face measures 9 centimeters.
What is the surface area of the triangular prism?
_____ square centimeters
To find the surface area of the triangular prism, we first need to find the area of the triangular faces and the rectangular faces separately, and then add them together.
1. Area of one triangular face:
The area of a triangle can be found using the formula: 0.5 * base * height.
In this case, the base is 6 cm and the height is 8 cm.
Area of one triangular face = 0.5 * 6 * 8 = 24 square centimeters.
Since there are two triangular faces on the triangular prism, the total area of the triangular faces is:
Total area of triangular faces = 2 * 24 = 48 square centimeters.
2. Area of one rectangular face:
The area of a rectangle can be found by multiplying the length by the width.
In this case, the length is 9 cm and the width is 6 cm.
Area of one rectangular face = 9 * 6 = 54 square centimeters.
Since there are three rectangular faces on the triangular prism, the total area of the rectangular faces is:
Total area of rectangular faces = 3 * 54 = 162 square centimeters.
Now, add the total area of the triangular faces and the total area of the rectangular faces to find the surface area of the triangular prism:
Surface area of the triangular prism = Total area of triangular faces + Total area of rectangular faces
Surface area = 48 + 162
Surface area = 210 square centimeters.
Therefore, the surface area of the triangular prism is 210 square centimeters.