To find the surface area of a rectangular prism, we need to find the total area of all six faces.
Since all the edge lengths measure 15.10 cm, the dimensions of the rectangular prism are 15.10 cm x 15.10 cm x 15.10 cm.
The surface area of a rectangular prism is given by the formula:
Surface Area = 2(lw + lh + wh)
Plugging in the given measurements:
Surface Area = 2(15.10 cm x 15.10 cm + 15.10 cm x 15.10 cm + 15.10 cm x 15.10 cm)
Surface Area = 2(228.01 cm2 + 228.01 cm2 + 228.01 cm2)
Surface Area = 2(684.03 cm2)
Surface Area = 1368.06 cm2
So, the surface area of the right rectangular prism is 1,368.06 cm2.
What is the surface area of a right rectangular prism where each edge length measures 15.10 cm?(1 point) Responses 1,350 cm2 1,350 cm squared 1,368.06 cm2 1,368.06 cm squared 8,208.36 cm2 8,208.36 cm squared 900 cm2
11 answers
A carry-on suitcase is 9.5 inches long, 16 inches wide, and 22.5 inches high. What is the surface area of the suitcase?(1 point) Responses 1,451.5 in.2 1 comma 451 point 5 in. squared 3,420 in.2 3 comma 420 in. squared 96 in.2 96 in. squared 725.75 in.2
To find the surface area of the suitcase, we need to find the total area of all six faces.
The dimensions of the suitcase are 9.5 inches x 16 inches x 22.5 inches.
The surface area of a rectangular prism is given by the formula:
Surface Area = 2(lw + lh + wh)
Plugging in the given measurements:
Surface Area = 2(9.5 in x 16 in + 9.5 in x 22.5 in + 16 in x 22.5 in)
Surface Area = 2(152 in² + 213.75 in² + 360 in²)
Surface Area = 2(725.75 in²)
Surface Area = 1,451.5 in²
So, the surface area of the carry-on suitcase is 1,451.5 in².
The dimensions of the suitcase are 9.5 inches x 16 inches x 22.5 inches.
The surface area of a rectangular prism is given by the formula:
Surface Area = 2(lw + lh + wh)
Plugging in the given measurements:
Surface Area = 2(9.5 in x 16 in + 9.5 in x 22.5 in + 16 in x 22.5 in)
Surface Area = 2(152 in² + 213.75 in² + 360 in²)
Surface Area = 2(725.75 in²)
Surface Area = 1,451.5 in²
So, the surface area of the carry-on suitcase is 1,451.5 in².
Find the surface area of a rectangular pyramid with these measurements: l = 15 m, w = 12 m, and h = 10 m. Express your answer as a decimal rounded to the nearest hundredth.(1 point) m2
To find the surface area of a rectangular pyramid, we need to find the area of the base and the area of the four triangular faces.
The dimensions of the rectangular base are 15 m x 12 m, so the base area is 15 m * 12 m = 180 m².
The area of each triangular face is given by the formula:
Triangle Area = (1/2) * base * height
For the triangular faces, the base and height are given as:
Base = 15 m
Height = 10 m
Therefore, the area of each triangular face is (1/2) * 15 m * 10 m = 75 m².
Since there are four triangular faces, the total area of the four triangular faces is 4 * 75 m² = 300 m².
The total surface area of the rectangular pyramid is then the sum of the base area and the area of the triangular faces:
Surface Area = base area + area of triangular faces = 180 m² + 300 m² = 480 m².
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is 480.00 m².
The dimensions of the rectangular base are 15 m x 12 m, so the base area is 15 m * 12 m = 180 m².
The area of each triangular face is given by the formula:
Triangle Area = (1/2) * base * height
For the triangular faces, the base and height are given as:
Base = 15 m
Height = 10 m
Therefore, the area of each triangular face is (1/2) * 15 m * 10 m = 75 m².
Since there are four triangular faces, the total area of the four triangular faces is 4 * 75 m² = 300 m².
The total surface area of the rectangular pyramid is then the sum of the base area and the area of the triangular faces:
Surface Area = base area + area of triangular faces = 180 m² + 300 m² = 480 m².
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is 480.00 m².
What is the surface area of a square pyramid where the base edge is 1.5 cm and the slant height is 4 cm? Round your answer to the nearest hundredth.(1 point) cm2
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
The base edge of this pyramid is 1.5 cm, so the area of the base is 1.5 cm * 1.5 cm = 2.25 cm².
The slant height is given as 4 cm. Since it's a square pyramid, the slant height is also the height of each triangular face.
For a triangular face with base length b and height h, the area is given by:
Triangle Area = (1/2) * base * height
For each triangular face in this pyramid, the base length is 1.5 cm and the height is 4 cm.
Therefore, the area of each triangular face is (1/2) * 1.5 cm * 4 cm = 3 cm².
Since there are four triangular faces, the total area of the four triangular faces is 4 * 3 cm² = 12 cm².
The total surface area of the square pyramid is then the sum of the base area and the area of the triangular faces:
Surface Area = base area + area of triangular faces = 2.25 cm² + 12 cm² = 14.25 cm².
Rounding to the nearest hundredth, the surface area of the square pyramid is 14.25 cm².
The base edge of this pyramid is 1.5 cm, so the area of the base is 1.5 cm * 1.5 cm = 2.25 cm².
The slant height is given as 4 cm. Since it's a square pyramid, the slant height is also the height of each triangular face.
For a triangular face with base length b and height h, the area is given by:
Triangle Area = (1/2) * base * height
For each triangular face in this pyramid, the base length is 1.5 cm and the height is 4 cm.
Therefore, the area of each triangular face is (1/2) * 1.5 cm * 4 cm = 3 cm².
Since there are four triangular faces, the total area of the four triangular faces is 4 * 3 cm² = 12 cm².
The total surface area of the square pyramid is then the sum of the base area and the area of the triangular faces:
Surface Area = base area + area of triangular faces = 2.25 cm² + 12 cm² = 14.25 cm².
Rounding to the nearest hundredth, the surface area of the square pyramid is 14.25 cm².
Niko has an outdoor play tent in the form of a regular triangular pyramid, covered in fabric on all four sides. The surface area of the tent is 100 ft.2 , the base is 6 ft., and the slant height is 8 ft. What is the height of the base to the nearest tenth?(1 point) Responses 372 ft. 372 ft. 9.3 ft. 9.3 ft. 6.5 ft. 6.5 ft. 57.3 ft.
To find the height of the base of the triangular pyramid, we need to use the formula for the surface area of a pyramid.
The formula for the surface area of a triangular pyramid is given by:
Surface Area = (l * p)/2 + B
Where:
l = slant height,
p = perimeter of the base, and
B = area of the base.
In this case, we have:
Surface Area = 100 ft²,
l = 8 ft,
B = (1/2) * base * h,
base = 6 ft,
and we need to find the height (h) of the base.
First, let's find the perimeter (p) of the base:
p = 3 * base = 3 * 6 ft = 18 ft.
Now, we can rearrange the formula for surface area to solve for h:
Surface Area = (l * p)/2 + B
100 ft² = (8 ft * 18 ft)/2 + (1/2) * 6 ft * h
100 ft² = 72 ft² + 3 ft * h
Rearranging the equation:
28 ft² = 3 ft * h
Dividing both sides by 3 ft:
h = 28 ft² / 3 ft ≈ 9.33 ft
Therefore, the height of the base of the triangular pyramid is approximately 9.3 ft to the nearest tenth.
The formula for the surface area of a triangular pyramid is given by:
Surface Area = (l * p)/2 + B
Where:
l = slant height,
p = perimeter of the base, and
B = area of the base.
In this case, we have:
Surface Area = 100 ft²,
l = 8 ft,
B = (1/2) * base * h,
base = 6 ft,
and we need to find the height (h) of the base.
First, let's find the perimeter (p) of the base:
p = 3 * base = 3 * 6 ft = 18 ft.
Now, we can rearrange the formula for surface area to solve for h:
Surface Area = (l * p)/2 + B
100 ft² = (8 ft * 18 ft)/2 + (1/2) * 6 ft * h
100 ft² = 72 ft² + 3 ft * h
Rearranging the equation:
28 ft² = 3 ft * h
Dividing both sides by 3 ft:
h = 28 ft² / 3 ft ≈ 9.33 ft
Therefore, the height of the base of the triangular pyramid is approximately 9.3 ft to the nearest tenth.
A metalworker is creating decorative points in the form of triangular pyramids to go on top of a fence she is building. She wants to know the surface area of each pyramid. Use the surface area formula to find the surface area of each pyramid based on the figure. (1 point)
I apologize, but without the specific dimensions or measurements of the triangular pyramid, I am unable to calculate the surface area. Could you please provide the necessary information, such as the lengths of the base and the slant height, in order for me to assist you further?