What is the surface area of a triangular prism with one side 6 cm one side 9 cm one side 10 cm and one side 8 cm in square centimeters
To find the surface area of a triangular prism, you need to calculate the area of each of the triangular faces and the area of the three rectangular faces, and then add them together.
The triangular faces have base and height given as 6 cm and 9 cm respectively:
Area of one triangular face = (1/2) * 6 * 9 = 27 square cm
Since there are two triangular faces, total area of both = 2 * 27 = 54 square cm
The third triangular face has base and height given as 9 cm and 10 cm:
Area of third triangular face = (1/2) * 9 * 10 = 45 square cm
The rectangular faces have dimensions given as 6 cm x 8 cm, 8 cm x 10 cm, and 6 cm x 10 cm:
Area of each rectangular face = length * width
Area of first rectangular face = 6 * 8 = 48 square cm
Area of second rectangular face = 8 * 10 = 80 square cm
Area of third rectangular face = 6 * 10 = 60 square cm
Add the areas of all the faces:
Total surface area = 54 + 45 + 48 + 80 + 60 = 287 square cm
Therefore, the surface area of the triangular prism is 287 square centimeters.