What is the surface area of the triangular prism?
(1 point)
An illustration shows a triangular prism. The front triangular face is visible. The right rectangular face is visible. The visible rectangular face has a width of 5 centimeters and length of 11 centimeters. The sides and edges that are not visible are indicated by dashed lines. The legs of the triangular face are labeled 3 centimeters and 4 centimeters. The hypotenuse shares the same label as the width of the visible rectangular face.
To find the surface area of a triangular prism, we need to calculate the areas of all the surfaces and then add them up.
1. The area of the front triangular face can be calculated using the formula for the area of a triangle: 1/2 * base * height. In this case, the base is 11 cm and the height is 4 cm (the longer leg of the triangle), so the area of the triangle is 1/2 * 11 * 4 = 22 square cm.
2. The area of the back triangular face will be the same as the front face, so it's also 22 square cm.
3. The area of the rectangular face can be calculated as length * width, which in this case is 11 cm * 5 cm = 55 square cm.
Now, add up the areas of all the surfaces:
22 square cm (front triangular face) + 22 square cm (back triangular face) + 55 square cm (rectangular face) = 99 square cm.
Therefore, the surface area of the triangular prism is 99 square cm.