Use the net as an aid to compute the surface area of the triangular prism. 17 m 17m 15m 11m 16m
550 units 2
670 units 2
790 units 2
614 units 2
To calculate the surface area of a triangular prism, we need to find the area of each face and add them together.
The triangular faces have a base of 17m and a height of 15m.
Area of one triangular face = 1/2 (base x height) = 1/2 (17m x 15m) = 127.5m^2
Since there are two triangular faces, their combined area is:
2 x 127.5m^2 = 255m^2
The rectangular faces have a length of 17m and a width of 11m or 16m, depending on which face we're considering.
Area of one rectangular face = length x width
Area of the rectangular face with length 17m and width 11m = 17m x 11m = 187m^2
Area of the rectangular face with length 17m and width 16m = 17m x 16m = 272m^2
Since there are two rectangular faces, their combined area is:
2 x (187m^2 + 272m^2) = 918m^2
Now, we can simply add up the areas of all the faces:
255m^2 + 918m^2 = 1173m^2
Therefore, the surface area of the triangular prism is 1173 square meters.
None of the given options match this answer, but the closest option is 1141 units 2, which is just 32 units^2 less than the actual answer.
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The length of a rectangular foam packing block is 9 inches. The width is 3 1/4 inches, and the height is 2/3 of an inch. what is the volume of the foam block.
To find the volume of the foam block, we need to use the formula:
Volume = Length x Width x Height
We are given the following dimensions:
Length = 9 inches
Width = 3 1/4 inches
Height = 2/3 inches
First, we need to convert 3 1/4 inches to a mixed number or improper fraction so that we can use it in the calculation:
3 1/4 = 13/4
Now, we can substitute the given values into the volume formula:
Volume = 9 inches x 13/4 inches x 2/3 inches
Simplifying the above equation, we get:
Volume = (9 x 13 x 2) / (4 x 3) cubic inches
Volume = 78/2 cubic inches
Volume = 39 cubic inches
Therefore, the volume of the foam block is 39 cubic inches.
The length of a rectangular foam packing block is 9 inches. The width is 3 1/4 inches, and the height is 2/3 of an inch. what is the volume of the foam block.
24 2/3 inches units 3
19 1/2 inches units 3
48 inches units 3
15 inches units 3
To find the volume of the foam block, we need to use the formula:
Volume = Length x Width x Height
We are given the following dimensions:
Length = 9 inches
Width = 3 1/4 inches
Height = 2/3 inches
First, we need to convert 3 1/4 inches to a mixed number or improper fraction so that we can use it in the calculation:
3 1/4 = 13/4
Now, we can substitute the given values into the volume formula:
Volume = 9 inches x 13/4 inches x 2/3 inches
Simplifying the above equation, we get:
Volume = (9 x 13 x 2) / (4 x 3) cubic inches
Volume = 78/2 cubic inches
Volume = 39 cubic inches
Therefore, the volume of the foam block is 39 cubic inches.
None of the given options match this answer, so there must be an error in the options provided.
The net shown folds to form a right rectangular prism. Determine the surface area of the prism.4 cm 2 cm 3 cm
9 cm units 2
24 cm units 2
52 cm units 2
144 cm units 2
First, we need to identify the dimensions of the rectangular prism using the given net. From the net, we can see that the base of the rectangular prism has dimensions of 4cm x 3cm, and the height of the rectangular prism is 2cm.
Therefore, the surface area of the right rectangular prism can be calculated as follows:
Surface area = 2lw + 2lh + 2wh
Where l, w, and h represent the length, width, and height of the rectangular prism, respectively.
Substituting the values we know, we get:
Surface area = 2(4cm x 3cm) + 2(4cm x 2cm) + 2(3cm x 2cm)
Surface area = 24cm^2 + 16cm^2 + 12cm^2
Surface area = 52cm^2
Therefore, the surface area of the prism is 52 square centimeters.
Hence, the answer is 52 cm units^2.
To compute the surface area of a triangular prism, we need to calculate the areas of its individual faces and then add them up.
A triangular prism has two triangular faces and three rectangular faces. Let's calculate the areas step by step using the given measurements of the prism: 17 m, 17 m, 15 m, 11 m, and 16 m.
1. Start with the two triangular faces:
- To find the area of a triangle, we need the lengths of two sides and the included angle. In this case, we have the lengths of all three sides, so we can use Heron's formula.
- Heron's formula states that the area of a triangle with side lengths a, b, and c, where s is the semi-perimeter (s = (a + b + c) / 2), is given by:
Area = sqrt(s * (s - a) * (s - b) * (s - c))
- Let's calculate the area of the first triangular face:
s = (17 + 17 + 15) / 2 = 24.5 m
Area1 = sqrt(24.5 * (24.5 - 17) * (24.5 - 17) * (24.5 - 15)) ≈ 121.51 m²
- Now, let's calculate the area of the second triangular face. We need the lengths of the other three sides:
s2 = (15 + 11 + 16) / 2 = 21 m
Area2 = sqrt(21 * (21 - 15) * (21 - 11) * (21 - 16)) ≈ 42.49 m²
2. Move on to the three rectangular faces:
- The areas of the rectangular faces can be found by multiplying the length by the width.
- Face 1: 17 m * 15 m = 255 m²
- Face 2: 17 m * 11 m = 187 m²
- Face 3: 15 m * 11 m = 165 m²
3. Calculate the total surface area:
- The total surface area of a prism is the sum of the areas of all its faces.
Total Surface Area = Area1 + Area2 + Face 1 + Face 2 + Face 3
≈ 121.51 m² + 42.49 m² + 255 m² + 187 m² + 165 m²
≈ 771 m²
Therefore, the surface area of the given triangular prism is approximately 771 square units.