Use Nets to Solve Triangular Problems Quick Check
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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
97.24 cm2
, 97.24 cm squared
573.24 cm2
, 573.24 cm squared
700.40 cm2
700.40 cm squared
603.16 cm2
, 603.16 cm squared
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=(12)(5)(6.5)
, upper S upper A equals left parenthesis Start Fraction 1 over 2 End Fraction right parenthesis left parenthesis 5 right parenthesis left parenthesis 6.5 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
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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
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
18.37 m2
, 18.37 m squared
14.63 m2
, 14.63 m squared
16.22 m2
16.22 m squared
12.98 m2
, 12.98 m squared
We first need to find the length and width of the base of the triangular prism. The width is the same as the thickness, which is 0.44 meters. To find the length, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are the dimensions of the rectangular base (which are equal since it's a square sandwich cut in half diagonally), and c is the hypotenuse of the triangular face (which is 5.1 meters).
We can solve for a (or b) as follows:
a^2 + a^2 = 5.1^2
2a^2 = 26.01
a^2 = 13.005
a = sqrt(13.005)
a ≈ 3.61 meters
So the dimensions of the base are approximately 3.61 meters by 0.44 meters.
Now we can use the formula for the surface area of a triangular prism:
SA = base area + lateral area
The base area is the area of the triangular base, which is:
(1/2)bh = (1/2)(3.61)(0.44) = 0.7934 m^2
The lateral area is the sum of the areas of the two congruent rectangular sides, which are:
2bh = 2(3.61)(3.6) = 25.98 m^2
So the total surface area is:
SA = 0.7934 + 25.98 ≈ 26.77 m^2
Rounded to two decimal places, the answer is 26.77 m^2.
Therefore, the correct response is:
26.77 m2
, 26.77 m squared
thats wrong
I apologize for the mistake. Let's try again.
The length and width of the rectangular base of the triangular prism are both half the width of the sandwich, which is 1.8 meters. Therefore, the base measures 1.8 meters by 1.8 meters.
To find the height of the triangular prism (which is also the height of the triangular faces), we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a and b are half the dimensions of the triangular face (since we cut the sandwich in half diagonally), and c is the hypotenuse, which is 5.1 meters.
We can solve for a (or b) as follows:
a^2 + a^2 = 5.1^2
2a^2 = 26.01
a^2 = 13.005
a = sqrt(13.005)/sqrt(2)
a ≈ 1.81 meters
So the height of the triangular prism is approximately 1.81 meters.
Now we can use the formula for the surface area of a triangular prism:
SA = base area + lateral area
The base area is the area of the rectangle, which is:
lw = 1.8(1.8) = 3.24 m^2
The lateral area is the sum of the areas of the two congruent triangular faces, which are:
(1/2)bh = (1/2)(1.81)(1.8) = 1.629 m^2
And then we have two lateral faces that are also congruent triangles with base 1.8m and height 3.6m
(1/2)bh = (1/2)(1.8)(3.6) = 3.24 m^2
So the total surface area is:
SA = 3.24 + 1.629 + 3.24 + 3.24 ≈ 11.35 m^2
Rounded to two decimal places, the answer is 11.35 m^2.
Therefore, the correct response is:
11.35 m2
, 11.35 m squared
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
25.41 in.2
, , 25.41 in. squared
25.08 in.2
25.08 in. squared
30.33 in.2
, 30.33 in. squared
24.75 in.2
, , 24.75 in. squared
To find the surface area of the triangular prism, we need to find the area of each face and then add them up.
The triangular prism has two congruent triangular faces and three rectangles.
To find the area of each triangular face, we can use the formula:
(1/2)bh
where b is the base (which is 5 inches) and h is the height of the triangular face (which is 1.5 inches). To find the height of the triangle, we can use the Pythagorean theorem:
a^2 + b^2 = c^2
where a is half the length of the base (since we have a right triangle), and c is the hypotenuse.
We can solve for a as follows:
a^2 + 1.5^2 = 5.22^2
a^2 = 5.22^2 - 1.5^2
a ≈ 4.824
So the height of the triangular face is approximately 4.824 inches.
Now we can find the area of each triangular face:
(1/2)bh = (1/2)(5)(4.824) ≈ 12.06 in^2
To find the area of each rectangular face, we can use the formula:
lw
where l is the length of the rectangle (which is 5 inches), and w is the width of the rectangle (which is the height of the triangular prism, which is 1.5 inches).
So the area of each rectangular face is:
lw = 5(1.5) = 7.5 in^2
Now we can find the total surface area:
SA = 2(12.06) + 3(7.5) ≈ 25.68 in^2
Rounded to two decimal places, the answer is 25.68 in^2.
Therefore, the correct response is:
25.68 in.2
, 25.68 in. squared
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
1,305.60 ft.2
1,305.60 ft. squared
1,215.60 ft.2
, 1,215.60 ft. squared
1,462.80 ft.2
, 1,462.80 ft. squared
982.8 ft.2