Use the image to answer the question.
A triangular prism. The front triangular face is visible. The right rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. 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?
Pls
To find the surface area of a triangular prism, you need to calculate the areas of the three rectangular faces and two triangular faces and add them together.
The formula for calculating the surface area of a triangular prism is:
Surface Area = 2(base area of triangle) + (perimeter of triangle x width) + (height of prism x perimeter of rectangle)
The base area of the triangle can be calculated using the formula for the area of a triangle:
Area = 1/2 x base x height
Area = 1/2 x 6 cm x 8 cm
Area = 24 cm^2
The perimeter of the triangle can be calculated by adding the three side lengths:
Perimeter = 6 cm + 8 cm + 10 cm
Perimeter = 24 cm
Plugging these values into the surface area formula:
Surface Area = 2(24 cm^2) + (24 cm x 9 cm) + (9 cm x 24 cm)
Surface Area = 48 cm^2 + 216 cm^2 + 216 cm^2
Surface Area = 480 cm^2
Therefore, the surface area of the triangular prism is 480 cm^2.