a triangular prism has bases that are equilateral triangles which statements are true about the surface area of the triangular prism? choose all that apply
all three rectangular faces have the same surface area
the surface area of each rectangular face is 66cm2
the combined surface area of one base is 15.6cm2
umm what ? no one is goona answer this?!
i need help
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What is the surface area of a rectangular prism with the numbers 24 36 and 54?
To find the surface area of a rectangular prism, you need to use the formula:
Surface Area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism, respectively.
Given the dimensions of the rectangular prism as 24, 36, and 54, we can substitute these values into the formula:
Surface Area = 2(24 x 36) + 2(24 x 54) + 2(36 x 54)
Surface Area = 17280 + 25920 + 38880
Surface Area = 82080 square units
Therefore, the surface area of the rectangular prism with dimensions 24, 36, and 54 is 82080 square units.
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You are drawing a net that shows a rectangular prism with an area of 52 square feet. If two of the rectangles in the net are 4 ft.×3 ft., what is the value of the third measurement you need to know to have an area of 52 square feet?
For a rectangular prism, the formula for finding the surface area is given as:
Surface Area = 2lw + 2lh + 2wh
Since we are given that two of the rectangles have dimensions of 4 ft. x 3 ft., we can assume that these represent the length and width dimensions. Let's call the missing dimension 'h'. Also, the total surface area is given as 52 square feet. Therefore, we can write the following equation:
2(4 ft.)(3 ft.) + 2(4 ft.)(h) + 2(3 ft.)(h) = 52 sq. ft.
Simplifying the equation, we get:
24 + 8h + 6h = 52
Combining like terms, we get:
14h = 28
Therefore, the missing dimension 'h' that we need to know to have an area of 52 square feet is:
h = 2
So, the dimensions of the rectangular prism are 4 ft. x 3 ft. x 2 ft.
what is the surface area of a triangular prism with the numbers 6 7 8 and 10?
To find the surface area of a triangular prism, you first need to find the area of the triangular bases, then find the area of each rectangular side, and finally add the two values together.
Given the base sides of the triangular prism with numbers 6, 7, and 8, we can first find the area of the triangles using Heron's Formula for the area of a triangle:
s = (6 + 7 + 8) / 2 = 10.5
Area of triangle = sqrt(s(s-6)(s-7)(s-8))
= sqrt(10.5(10.5-6)(10.5-7)(10.5-8))
= sqrt(10.5 * 4.5 * 3.5 * 2.5)
= 21sqrt(5) square units
Next, we find the area of the rectangular sides. We can split the rectangular side into two rectangles: one rectangle with dimensions 6 x 10 and another rectangle with dimensions 7 x 10. The area of each rectangular side is just the product of their dimensions:
Area of 6 x 10 rectangle = 6 x 10 = 60 square units
Area of 7 x 10 rectangle = 7 x 10 = 70 square units
Finally, we add the area of the two triangles and the two rectangles:
Surface area = 2(21sqrt(5)) + 2(60 + 70)
= 42sqrt(5) + 260
≈ 310.55 square units (rounded to two decimal places)
Therefore, the surface area of the triangular prism with the numbers 6, 7, 8, and 10 is approximately 310.55 square units.
what is the surface area of a triangular prism with the numbers 49 56 56 60 and 60
To find the surface area of a triangular prism, you first need to find the area of the triangular bases, then find the area of each rectangular side, and finally add the two values together.
Given the base sides of the triangular prism with numbers 49, 56, 56, 60, and 60, we can first find the area of the triangles using Heron's Formula for the area of a triangle:
s = (56 + 56 + 49) / 2 = 80.5
Area of triangle = sqrt(s(s-56)(s-56)(s-49))
= sqrt(80.5(80.5-56)(80.5-56)(80.5-49))
= sqrt(80.5 * 24.5 * 24.5 * 31.5)
≈ 1355.08 square units
s = (60 + 56 + 49) / 2 = 82.5
Area of triangle = sqrt(s(s-60)(s-56)(s-49))
= sqrt(82.5(82.5-60)(82.5-56)(82.5-49))
= sqrt(82.5 * 22.5 * 26.5 * 33.5)
≈ 1517.71 square units
Next, we find the area of the rectangular sides. We can split the rectangular side into two rectangles: one rectangle with dimensions 49 x 60 and another rectangle with dimensions 56 x 60. The area of each rectangular side is just the product of their dimensions:
Area of 49 x 60 rectangle = 49 x 60 = 2940 square units
Area of 56 x 60 rectangle = 56 x 60 = 3360 square units
Finally, we add the area of the two triangles and the two rectangles:
Surface area = 2(1355.08 + 1517.71) + 2(2940 + 3360)
= 5446.58 square units
Therefore, the surface area of the triangular prism with the numbers 49, 56, 56, 60, and 60 is 5446.58 square units.
Kym’s sawhorse is 39 inches tall, 27 inches long, and 19 inches wide. Its diagonal measurement, or the hypotenuse, is 40.14 inches. What is its total surface area? Round your answer to the nearest hundredth.
To find the total surface area of Kym's sawhorse, we need to find the areas of each of its faces and add them up.
The sawhorse has two pairs of identical rectangular faces, one pair on each side. The area of each of these faces is just the product of the length and width. Therefore, the total area of these four rectangular faces is:
Total area of rectangular faces = 2(27 x 19) + 2(39 x 19)
= 1080 square inches
The sawhorse also has two triangular faces on each end. We can use the Pythagorean theorem to find the height of each triangular face. The hypotenuse is given as 40.14 inches, and the other two sides have lengths of 27 and 19 inches. Let's call the missing height 'h'. Then we have:
h^2 + 19^2 = 40.14^2 - 27^2
h^2 = 953.8596 - 729
h^2 = 224.8596
h ≈ 14.99 inches
Therefore, each triangular face has a height of approximately 14.99 inches. The area of each triangular face is given as:
Area of each triangular face = (1/2) x base x height
= (1/2) x 27 x 14.99
≈ 202.80 square inches
Therefore, the total area of the two triangular faces is:
Total area of triangular faces = 2(202.80)
= 405.60 square inches
Finally, we add the areas of the rectangular and triangular faces to get the total surface area of the sawhorse:
Total surface area = 1080 + 405.60
= 1485.60 square inches
Therefore, the total surface area of Kym's sawhorse is approximately 1485.60 square inches.