Use the image to answer the question.
An illustration shows a 3 D rectangular base prism with two opposite triangular faces. A point is shown on the top edge and one each on the lateral edge of the front triangular face. The three dots are joined to form a triangle.
What is the two-dimensional shape created by the sliced object?
triangle
hexagon
parallelogram
rectangle
triangle
What is a two-dimensional representation of a three-dimensional figure?
a net
a square
a cube
a rectangle
a net
What is the missing length of a rectangular prism where the height and width are both 9 cm and the surface area is 432 cm2?
Let the length of the rectangular prism be "L".
The formula for the surface area of a rectangular prism is:
S = 2lw + 2lh + 2wh
Substituting the given values, we get:
432 = 2(9)(L) + 2(9)(9) + 2(L)(9)
Simplifying,
432 = 18L + 162 + 18L
432 = 36L + 162
270 = 36L
L = 7.5
Therefore, the missing length of the rectangular prism is 7.5 cm.
Fill in the blanks to complete the formula for the surface area of a triangular prism.
The surface area of a triangular prism is S.A.= +(S1+S2+S3)
(b × h) +(S1+S2+S3)
Fill in the blanks to complete the formula for the surface area of a triangular prism.
The surface area of a triangular prism is S.A.=
+(S1+S2+S3)
S.A. = (b × h) + (S1+S2+S3)
that's not really an answer
My apologies. Here is the complete formula:
The surface area of a triangular prism is given by the formula:
S.A. = (base × height) + (perimeter of base × height of prism)
or S.A. = (b × h) + (S1+S2+S3)
where
- b is the length of the base of the triangle
- h is the height of the triangle
- S1, S2, and S3 are the areas of the three rectangular faces of the prism, which can be found using base times height.
so then, what do i put for s1, s2, and s3?
To find the areas of the three rectangular faces (S1, S2, and S3), you will need to know the dimensions of the base triangle and the height of the prism. Let's say the base of the triangle has a length of "b" and a height of "h".
Then, the three rectangular faces will have the following dimensions:
- Face S1: Length = b, Width = height of the prism
- Face S2: Length = perimeter of base, Width = height of the prism
- Face S3: Length = b, Width = height of the prism
So, you can find S1, S2, and S3 by multiplying the corresponding lengths and widths as:
- S1 = b × height of the prism
- S2 = perimeter of base × height of the prism
- S3 = b × height of the prism
Then substitute these values in the formula S.A. = (b × h) + (S1+S2+S3) to calculate the surface area of the triangular prism.
Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The right rectangular face is visible. The visible rectangular face has a width of 5 centimeters and length of 11 centimeters. The sides and edges that are not visible are indicated by dashed lines. The legs of the triangular face are labeled 3 centimeters and 4 centimeters. The hypotenuse shares the same label as the width of the visible rectangular face.
What is the surface area of the triangular prism?
? square centimeters
To find the surface area of the triangular prism, we need to calculate the area of all the faces and add them up.
- Area of the front triangular face = (1/2) × base × height = (1/2) × 3 × 4 = 6 square centimeters.
- Area of the back triangular face (which is congruent to the front face) = 6 square centimeters.
- Area of the left rectangular face = length × width = 5 × 4 = 20 square centimeters.
- Area of the right rectangular face (which is congruent to the left face) = 20 square centimeters.
- Area of the top rectangular face (base of the triangle) = length × width = 5 × 11 = 55 square centimeters.
- Area of the bottom rectangular face (which is congruent to the top face) = 55 square centimeters.
So, the total surface area of the triangular prism is:
6 + 6 + 20 + 20 + 55 + 55 = 162 square centimeters.
Therefore, the surface area of the triangular prism is 162 square centimeters.
An illustration shows a rectangular prism with its length measuring 17 centimeters, width measuring 10 centimeters, and height measuring 4 centimeters. The edges that are not visible are marked as dashed lines.
Jerry wants to wrap a present in a box for his mother. The box measures 10 cm wide, 4 cm high, and 17 cm long. How much wrapping paper will Jerry need to wrap the present?
(1 point)
surface area = ? cm2
To find the surface area of the rectangular prism (i.e., the wrapping paper needed), we need to add up the areas of all six rectangular faces.
- Area of the front and back faces = length × height = 17 cm × 4 cm = 68 cm² × 2 faces = 136 cm²
- Area of the top and bottom faces = width × length = 10 cm × 17 cm = 170 cm² × 2 faces = 340 cm²
- Area of the left and right faces = width × height = 10 cm × 4 cm = 40 cm² × 2 faces = 80 cm²
Therefore, the total surface area is:
136 cm² + 340 cm² + 80 cm² = 556 cm²
So, Jerry will need approximately 556 square centimeters of wrapping paper to wrap the present.
Use the image to answer the question.
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 30.5 centimeters and 27.9 centimeters. The perpendicular side of the triangular face measures 5.1 centimeter and the hypotenuse measures 28.4 centimeter.
How much book cover material is needed to cover the three-ring binder? Round your answer to the nearest whole number.
(1 point)
To calculate the amount of book cover material needed to cover the three-ring binder, we need to find the surface area of the triangular prism.
The surface area of a triangular prism is given by the formula:
S.A. = (base × height) + (perimeter of base × height of prism)
In this case, the base of the triangle is 27.9 cm and the height of the triangle is 5.1 cm. So, the area of the triangular face is:
(1/2) × 27.9 cm × 5.1 cm = 70.695 cm²
The perimeter of the base is:
27.9 cm + 30.5 cm + 28.4 cm = 86.8 cm
The height of the prism is also 5.1 cm.
So, the surface area of the triangular prism is:
S.A. = (27.9 cm × 5.1 cm) + (86.8 cm × 5.1 cm) = 437.88 cm²
Therefore, Jerry will need approximately 438 square centimeters of book cover material to cover the three-ring binder. Rounded to the nearest whole number, this is 438 cm².
Use the image to answer the question.
An illustration shows a 3 D triangular prism with the triangular face as a right triangle. The edges that are not visible are represented by dashed lines. The length and base of the triangular prism measures 30.5 centimeters and 27.9 centimeters. The perpendicular side of the triangular face measures 5.1 centimeter and the hypotenuse measures 28.4 centimeter.
How much book cover material is needed to cover the three-ring binder? Round your answer to the nearest whole number.
(1 point)
S.A. = ? cm2
To calculate the surface area of the triangular prism, we need to use the formula:
S.A. = (base × height) + (perimeter of base × height of prism)
Here, the base of the triangle has a length of 27.9 cm and a height of 5.1 cm. Therefore, the area of the triangular face is:
(1/2) × 27.9 cm × 5.1 cm = 70.695 cm²
The perimeter of the base triangle is:
27.9 cm + 30.5 cm + 28.4 cm = 86.8 cm
The height of the triangular prism is also 5.1 cm.
So, the surface area of the triangular prism is:
S.A. = (27.9 cm × 5.1 cm) + (86.8 cm × 5.1 cm) = 437.88 cm²
Rounding this to the nearest whole number, we get:
S.A. = 438 cm²
Therefore, the surface area of the triangular prism (and the amount of book cover material needed to cover the three-ring binder) is approximately 438 square centimeters.
What is the shape of the base of a rectangular pyramid?
triangle
pyramid
vertex
rectangle
rectangle
Use the image to answer the question.
An illustration shows a slide slice where a triangular plane with a square frame is inserted into a 3 D pyramid through one of the edges. The plane is positioned till the apex is reached and the middle triangular portion of the pyramid is highlighted.
What two-dimensional shape is created by slicing a right rectangular pyramid perpendicular to the base?
trapezoid
square
triangle
rectangle
rectangle
An illustration shows a pyramid with a rectangular base of length 6 meters and width 2 meters. The perpendicular height from the apex to the center of the base is labeled 8.8 meters. The slant height from the apex to the center of the width of the rectangle is labeled 9 meters. Both heights are drawn as dotted lines. The sides that are not visible are shown in dashed lines.
What is the length of the pyramid?
? m
To find the length of the pyramid, we need to use the Pythagorean theorem since we are given the perpendicular height and the slant height.
The Pythagorean theorem states that:
c² = a² + b²
where c is the hypotenuse (in this case, the length of the pyramid), and a and b are the other two sides of the right triangle.
In our case, the perpendicular height (a) is 8.8 meters, and the slant height (b) is 9 meters. Therefore, we can write:
c² = a² + b²
c² = (8.8 m)² + (9 m)²
c² = 77.44 m² + 81 m²
c² = 158.44 m²
Taking the square root of both sides, we get:
c = sqrt(158.44)
c ≈ 12.6 m
Therefore, the length of the pyramid is approximately 12.6 meters.
An illustration shows a pyramid with a rectangular base. The length of the base is labeled 14 centimeters and the width as 12 centimeters. The perpendicular heights from the apex to the base length of 14 is 10 centimeters and to the base width of 12 is 10.6 centimeters. The perpendicular heights are denoted by two right angle symbols on two of the lateral faces from the apex to the base by dashed lines.
What is the surface area of the rectangular pyramid?
To find the surface area of the rectangular pyramid, we need to find the area of the four triangular faces and the rectangular base and add them up.
First, we will find the area of one triangular face.
The area of a triangle is given by the formula:
A = (1/2) × base × height
For one triangular face, the base is 14 cm and the height is 10 cm. So, the area of one triangular face is:
A = (1/2) × 14 cm × 10 cm = 70 cm²
Since there are four triangular faces, the total area of the triangular faces is:
4 × 70 cm² = 280 cm²
The area of the rectangular base is:
A = length × width = 14 cm × 12 cm = 168 cm²
Therefore, the total surface area of the rectangular pyramid is:
280 cm² + 168 cm² = 448 cm²
So, the surface area of the rectangular pyramid is 448 square centimeters.
An illustration shows a three dimensional composite figure formed by a right triangular prism placed on top of a rectangular prism. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 12 feet and a height of 8 feet. The width of the rectangular prism is not shown. The edges of the hidden side face of the right triangular prism align perfectly with the edges of the hidden top face of the rectangular prism. The right triangular prism is aligned to the left of the rectangular prism. The height of the right triangular prism is not shown. The total height of the left side of the figure is 20 feet. The right triangular prism has a width of 8 feet. The hypotenuse side of the right triangular prism has a length of 15 feet.
What is the surface area of the figure?
To find the surface area of the composite figure, we need to find the surface area of each individual prism and then add them up.
For the rectangular prism, we are given the length, height, and the width is not shown. However, we know that the top face of the rectangular prism aligns perfectly with the hidden face of the right triangular prism, which has a width of 8 feet. Therefore, the width of the rectangular prism must also be 8 feet.
The surface area of a rectangular prism is given by the formula:
S.A. = 2lw + 2lh + 2wh
In this case, the length is 12 feet, the height is 8 feet, and the width is 8 feet. So, the surface area of the rectangular prism is:
S.A. = 2(12 ft × 8 ft) + 2(12 ft × 8 ft) + 2(8 ft × 8 ft)
S.A. = 384 ft² + 192 ft² + 128 ft²
S.A. = 704 ft²
For the right triangular prism, we are given the width, the hypotenuse, and the height is not shown. However, we can use the Pythagorean theorem to find the height:
h² = c² - a² - b²
where c is the hypotenuse (15 feet), a is one leg of the triangle (8 feet), and b is the height of the right triangular prism that we need to find.
Plugging in the values, we get:
h² = 15² - 8² - b²
h² = 175
Taking the square root of both sides, we get:
h = sqrt(175)
h = 5sqrt(7)
So, the height of the right triangular prism is 5sqrt(7) feet.
The surface area of a right triangular prism is given by the formula:
S.A. = 2B + Ph
where B is the area of the triangular base, P is the perimeter of the base, and h is the height of the prism.
In this case, the base is a right triangle with legs of 8 feet and 15 feet, so its area is:
B = (1/2) × 8 ft × 15 ft
B = 60 ft²
The perimeter of the base is:
P = a + b + c
P = 8 ft + 15 ft + 17 ft
P = 40 ft
The height of the right triangular prism is 5sqrt(7) feet.
Therefore, the surface area of the right triangular prism is:
S.A. = 2(60 ft²) + 40 ft × 5sqrt(7) ft
S.A. = 120 ft² + 200sqrt(7) ft²
So, the total surface area of the composite figure is:
S.A. = 704 ft² + 120 ft² + 200sqrt(7) ft²
S.A. ≈ 1257.1 ft²
Therefore, the surface area of the composite figure is approximately 1257.1 square feet.
An illustration shows a 3-dimensional vertical rectangular prism that appears as the letter upper C, with a rectangular portion removed from the right center. The rectangular prism is 15 feet high, 10 feet wide, and 1 foot deep. The width of the portion removed from the middle on the right side is 7 feet across. The height of the remaining two arms left at the top and bottom is 4 feet each.
In Los Cabos, Mexico, there is a big sculpture of block letters that welcomes you. The image shows the letter C. What is its surface area?
(1 point)
? ft.2
To find the surface area of the block letter C, we need to find the area of each face and add them up.
There are five rectangular faces in this block letter C (three on the front, one on the top, and one at the back).
The front face at the top is 4 feet high and 7 feet wide, so its area is:
A = 4 ft × 7 ft = 28 ft²
The front face in the middle is 15 feet high and 1 foot wide, so its area is:
A = 15 ft × 1 ft = 15 ft²
The front face at the bottom is 4 feet
Solve the problem. The surface area of a square pyramid is 116 in.2 and the total area of the pyramid’s four triangular faces is 80 in.2
What is the length of one of the sides? Show your work.
The surface area of a square pyramid is 116 in.2 and the total area of the pyramid’s four triangular faces is 80 in.2
What is the length of one of the sides?