what is the two dimensional representation of a three dimensional figure?
a triangle
a rectangle
a net
a triangular prism
a net
which of the following describes a valid method for calculating the surface area of a triangular prism?
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of three times the area of one triangle and twice the area of one rectangle.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of one triangle and three times the area of one rectangle.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The left rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. All sides of the triangle measure 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 8 centimeters. The width of the rectangular face measures 6 centimeters.
280 square centimeters
320 square centimeters
180 square centimeters
260 square centimeters
To calculate the surface area of a triangular prism, we need to find the areas of all the faces and then add them up.
Front triangular face:
Area = 1/2 * base * height
Area = 1/2 * 10 cm * 8 cm
Area = 40 square cm
Two back triangular faces (same area as front face):
2 * 40 square cm = 80 square cm
Two rectangular faces:
Area = length * width
Area = 10 cm * 6 cm
Area = 60 square cm
Total surface area = Front triangular face + Two back triangular faces + Two rectangular faces
Total surface area = 40 square cm + 80 square cm + 60 square cm
Total surface area = 180 square centimeters
Therefore, the surface area of the triangular prism is 180 square centimeters.
are you sure?
Let's recalculate the surface area of the triangular prism given the measurements provided.
Front triangular face:
Area = (1/2) * base * height
Area = (1/2) * 10 cm * 8 cm
Area = 40 square cm
Two back triangular faces (same area as front face):
2 * 40 square cm = 80 square cm
Two rectangular faces:
Area = length * width
Area = 10 cm * 6 cm
Area = 60 square cm
Total surface area = Front triangular face + Two back triangular faces + Two rectangular faces
Total surface area = 40 square cm + 80 square cm + 60 square cm
Total surface area = 180 square centimeters
Therefore, the surface area of the triangular prism is 180 square centimeters.
I apologize for the oversight in my previous response, and I can confirm that the correct calculated surface area is indeed 180 square centimeters.