What is a two-dimensional representation of a three-dimensional figure?
a net
a triangle
a triangular prism
a rectangle
net
Which of the following describes a valid method for calculating the surface area of a triangular prism?
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 all five shapes.
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 twice 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.
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.
Solve for the surface area of the triangular prism.
280 square centimeters
260 square centimeters
320 square centimeters
180 square centimeters
260 square centimeters
To find the surface area of the triangular prism, we need to find the areas of all the faces and add them up.
The front triangular face has base 10 cm and height 8 cm. So its area is 1/2 x 10 cm x 8 cm = 40 square cm.
The left rectangular face has length 8 cm and width 6 cm. So its area is 8 cm x 6 cm = 48 square cm.
The right rectangular face is identical to the left one, so its area is also 48 square cm.
The top and bottom faces are congruent triangles with base 10 cm and height 6 cm. So each one has area 1/2 x 10 cm x 6 cm = 30 square cm. Together, they have total area 2 x 30 square cm = 60 square cm.
Adding up all the areas, we get 40 + 48 + 48 + 60 = 196 square cm. But remember that we need to also account for the areas that are not visible in the image. Since the triangular prism is a closed solid, each of the rectangular faces will have a corresponding face on the right side and back side of the prism. So we need to double their combined area of 48 square cm, which gives us 96 square cm.
Adding the visible and invisible areas, we get a total surface area of 196 + 96 = 292 square cm.
Surface Area of Triangular Prisms Quick Check
4 of 54 of 5 Items
Question
Use the image to answer the question.
An illustration shows 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 and right side of the triangle measure 17 meters. The perpendicular height from the top vertex of the triangle to the base measures 15 meters. The base of the triangle measures 16 meters. The width of the rectangular face measures 11 meters.
What is the surface area of the net of the triangular prism?
779 square meters
768 square meters
822 square meters
790 square meters
Use the image to answer the question.
An illustration shows 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 and right side of the triangle measure 17 meters. The perpendicular height from the top vertex of the triangle to the base measures 15 meters. The base of the triangle measures 16 meters. The width of the rectangular face measures 11 meters.
What is the surface area of the net of the triangular prism?
779 square meters
768 square meters
822 square meters
790 square meters
Use the image to answer the question.
An illustration shows 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 10 centimeters. The right side of the triangle also measures 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 6 centimeters. The base of the triangle measures 8 centimeters.
What is the missing length l
of the triangular prism if the surface area is 524 square centimeters?
16 cm
17 cm
8 cm
10 cm
768 square meters
To find the surface area of the triangular prism, we need to find the areas of all the faces and add them up.
The front triangular face has base 16 m and height 15 m. So its area is 1/2 x 16 m x 15 m = 120 square m.
The right rectangular face has length 15 m and width 11 m. So its area is 15 m x 11 m = 165 square m.
The left rectangular face is identical to the right one, so its area is also 165 square m.
The top and bottom faces are congruent triangles with base 16 m and height 17 m. So each one has area 1/2 x 16 m x 17 m = 136 square m. Together, they have total area 2 x 136 square m = 272 square m.
Adding up all the areas, we get 120 + 165 + 165 + 272 = 722 square m. But remember that we need to also account for the areas that are not visible in the image. Since the triangular prism is a closed solid, each of the rectangular faces will have a corresponding face on the opposite side of the prism. So we need to double their combined area of 330 square m, which gives us 660 square m.
Adding the visible and invisible areas, we get a total surface area of 722 + 660 = 1382 square m. But this is the surface area of the solid prism. The net of the prism is just the sum of the areas of the five faces that are visible in the image, which is 120 + 165 = 285 square m.