Use Nets to Solve Triangular Problems Quick Check
1 of 51 of 5 Items
Question
Use the image to answer the question.
An illustration shows a triangular prism placed sideways with one of its rectangular faces as the base. Dimensions are labeled. The length and width of the rectangular base are 17 centimeters and 13 centimeters respectively. The face visible in front appears as a triangle. The base width of the triangle is 13 centimeters. The perpendicular leg of the triangle is 7.48 centimeters and the slanting leg (hypotenuse) is 15 centimeters. The edges that are not visible are represented by dashed lines.
Apply the technique of using nets to find the surface area of this triangular prism. Your answer should have two decimal places.
(1 point)
Responses
603.16 cm2
603.16 cm squared
97.24 cm2
97.24 cm squared
573.24 cm2
573.24 cm squared
700.40 cm2
700.40 cm squared
9 answers
603.16 cm2
Use the image to answer the question.
An illustration shows a 2 D net of a triangular prism with all of its sides open and visible. Dimensions are labeled. The parts that are not visible in 3 D view are marked with dashed lines. It appears as three vertical rectangles placed vertically. The length and width of the top rectangle are 6.5 feet and 5 feet respectively. The length and width of the middle rectangle are 5.5 feet and 5 feet respectively. The length of the bottom rectangle is 5 feet. Two identical triangles adjoin the middle rectangle on both sides with legs measuring 3.5 feet and 5.5 feet. The hypotenuse measures 6.5 feet.
Write an equation for the surface area of both triangular bases of the net.
(1 point)
Responses
SA=12(3.5)(5)
upper S upper A equals Start Fraction 1 over 2 End Fraction left parenthesis 3.5 right parenthesis left parenthesis 5 right parenthesis
SA=2(12)(3.5)(5.5)
upper S upper A equals 2 left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis left parenthesis 3.5 right parenthesis left parenthesis 5.5 right parenthesis
SA=2(12)(6.1)(3.5)
upper S upper A equals 2 left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis left parenthesis 6.1 right parenthesis left parenthesis 3.5 right parenthesis
SA=(12)(5)(6.5)
An illustration shows a 2 D net of a triangular prism with all of its sides open and visible. Dimensions are labeled. The parts that are not visible in 3 D view are marked with dashed lines. It appears as three vertical rectangles placed vertically. The length and width of the top rectangle are 6.5 feet and 5 feet respectively. The length and width of the middle rectangle are 5.5 feet and 5 feet respectively. The length of the bottom rectangle is 5 feet. Two identical triangles adjoin the middle rectangle on both sides with legs measuring 3.5 feet and 5.5 feet. The hypotenuse measures 6.5 feet.
Write an equation for the surface area of both triangular bases of the net.
(1 point)
Responses
SA=12(3.5)(5)
upper S upper A equals Start Fraction 1 over 2 End Fraction left parenthesis 3.5 right parenthesis left parenthesis 5 right parenthesis
SA=2(12)(3.5)(5.5)
upper S upper A equals 2 left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis left parenthesis 3.5 right parenthesis left parenthesis 5.5 right parenthesis
SA=2(12)(6.1)(3.5)
upper S upper A equals 2 left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis left parenthesis 6.1 right parenthesis left parenthesis 3.5 right parenthesis
SA=(12)(5)(6.5)
upper S upper A equals 2 left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis left parenthesis 3.5 right parenthesis left parenthesis 5.5 right parenthesis
Use Nets to Solve Triangular Problems Quick Check
3 of 53 of 5 Items
Question
The 2005 world record for the longest sandwich is 3.6 meters with a width of 3.6 meters and a thickness of 0.44 meters. If you cut the sandwich in half diagonally, it would create a triangular prism with a hypotenuse of 5.1 meters. Apply the technique of using nets to find the surface area.(1 point)
Responses
14.63 m2
14.63 m squared
12.98 m2
12.98 m squared
16.22 m2
16.22 m squared
18.37 m2
18.37 m squared
3 of 53 of 5 Items
Question
The 2005 world record for the longest sandwich is 3.6 meters with a width of 3.6 meters and a thickness of 0.44 meters. If you cut the sandwich in half diagonally, it would create a triangular prism with a hypotenuse of 5.1 meters. Apply the technique of using nets to find the surface area.(1 point)
Responses
14.63 m2
14.63 m squared
12.98 m2
12.98 m squared
16.22 m2
16.22 m squared
18.37 m2
18.37 m squared
12.98 m2
A triangular prism has a height of 1.5 inches and right triangular bases with a height of 1.5 inches, length of 5 inches, and a hypotenuse measuring 5.22 inches. What is the prism's surface area? (1 point)
Responses
30.33 in.2
30.33 in. squared
25.41 in.2
25.41 in. squared
25.08 in.2
25.08 in. squared
24.75 in.2
Responses
30.33 in.2
30.33 in. squared
25.41 in.2
25.41 in. squared
25.08 in.2
25.08 in. squared
24.75 in.2
30.33 in.2
Calculate the surface area of a triangular prism shaped tent if the height is 9 ft., the length is 24 ft., the width is 20 ft., and the hypotenuse of the cover is 13.45 ft.(1 point)
Responses
982.8 ft.2
982.8 ft. squared
1,462.80 ft.2
1,462.80 ft. squared
1,305.60 ft.2
1,305.60 ft. squared
1,215.60 ft.2
1,215.60 ft. squared
Responses
982.8 ft.2
982.8 ft. squared
1,462.80 ft.2
1,462.80 ft. squared
1,305.60 ft.2
1,305.60 ft. squared
1,215.60 ft.2
1,215.60 ft. squared
To calculate the surface area of a triangular prism, we need to find the areas of the two triangular bases and the three rectangular faces.
Given:
- Height (h) = 9 ft.
- Length (l) = 24 ft.
- Width (w) = 20 ft.
- Hypotenuse of the cover = 13.45 ft.
The triangular base is a right triangle with l = 24 ft., w = 20 ft., and hypotenuse h = 13.45 ft.
Using the Pythagorean theorem, we can find the height of the triangle base:
h^2 = l^2 + w^2
h^2 = 24^2 + 20^2
h^2 = 576 + 400
h^2 = 976
h ≈ √976
h ≈ 31.24 ft.
Now we can calculate the surface area:
1. Calculate the area of the two triangular bases:
Base Area = (1/2) * base * height
Base Area = (1/2) * 24 * 20 = 240 ft²
2. Calculate the area of the three rectangular faces:
Rectangular Face 1:
Area = length * height = 24 * 9 = 216 ft²
Rectangular Face 2:
Area = width * height = 20 * 9 = 180 ft²
Rectangular Face 3:
Area = hypotenuse * height = 13.45 * 9 = 121.05 ft²
Total Surface Area = 2(Base Area) + 3(Sum of Rectangular Faces)
Total Surface Area = 2(240) + 3(216 + 180 + 121.05)
Total Surface Area = 480 + 1535.05
Total Surface Area ≈ 2015.05 ft²
Therefore, the surface area of the triangular prism-shaped tent is approximately 2015.05 ft².
Given:
- Height (h) = 9 ft.
- Length (l) = 24 ft.
- Width (w) = 20 ft.
- Hypotenuse of the cover = 13.45 ft.
The triangular base is a right triangle with l = 24 ft., w = 20 ft., and hypotenuse h = 13.45 ft.
Using the Pythagorean theorem, we can find the height of the triangle base:
h^2 = l^2 + w^2
h^2 = 24^2 + 20^2
h^2 = 576 + 400
h^2 = 976
h ≈ √976
h ≈ 31.24 ft.
Now we can calculate the surface area:
1. Calculate the area of the two triangular bases:
Base Area = (1/2) * base * height
Base Area = (1/2) * 24 * 20 = 240 ft²
2. Calculate the area of the three rectangular faces:
Rectangular Face 1:
Area = length * height = 24 * 9 = 216 ft²
Rectangular Face 2:
Area = width * height = 20 * 9 = 180 ft²
Rectangular Face 3:
Area = hypotenuse * height = 13.45 * 9 = 121.05 ft²
Total Surface Area = 2(Base Area) + 3(Sum of Rectangular Faces)
Total Surface Area = 2(240) + 3(216 + 180 + 121.05)
Total Surface Area = 480 + 1535.05
Total Surface Area ≈ 2015.05 ft²
Therefore, the surface area of the triangular prism-shaped tent is approximately 2015.05 ft².
1 answer