To find the surface area of a rectangular pyramid, you need to find the area of each face and add them together.
The rectangular pyramid has 5 faces: one base and four triangles.
The area of the base is found by multiplying the length and width:
Base area = l * w = 13 cm * 11 cm = 143 cm^2
The area of each triangle face can be found using the formula (1/2) * base * height:
Triangle area = (1/2) * l * h
1st triangle area = (1/2) * 13 cm * 8 cm = 52 cm^2
2nd triangle area = (1/2) * 13 cm * 8 cm = 52 cm^2
3rd triangle area = (1/2) * 11 cm * 8 cm = 44 cm^2
4th triangle area = (1/2) * 11 cm * 8 cm = 44 cm^2
Now, add the areas of all the faces together to find the surface area:
Surface area = Base area + 2 * Triangle area
Surface area = 143 cm^2 + 52 cm^2 + 52 cm^2 + 44 cm^2 + 44 cm^2
Surface area = 335 cm^2
Therefore, the surface area of the rectangular pyramid is approximately 335 cm^2.
Find the surface area of a rectangular pyramid with these measurements: l = 13 cm, w = 11 cm, and h = 8 cm. Express your answer as a decimal rounded to the nearest hundredth. WHAT IS THE ANSWERRRR
7 answers
incorrect
Apologies for the mistake. Let's calculate the correct surface area of the rectangular pyramid.
The base area of the pyramid is given by length times width:
Base area = l * w = 13 cm * 11 cm = 143 cm^2
Now, let's calculate the area of each triangular face. Since the base of the pyramid is rectangular, the triangular faces are all congruent right triangles.
The area of a right triangle is given by (1/2) * base * height:
Triangle area = (1/2) * l * h
First, let's calculate the area of the triangle with a base of length 13 cm and height 8 cm:
Triangle area = (1/2) * 13 cm * 8 cm = 52 cm^2
Next, let's calculate the area of the triangle with a base of length 11 cm and height 8 cm:
Triangle area = (1/2) * 11 cm * 8 cm = 44 cm^2
Since the pyramid has four triangular faces, we need to multiply the area by 4 to account for all faces:
Total triangle area = 4 * (52 cm^2 + 44 cm^2) = 4 * 96 cm^2 = 384 cm^2
Finally, we can find the surface area by adding the base area and the total triangle area:
Surface area = Base area + Total triangle area = 143 cm^2 + 384 cm^2 = 527 cm^2
Therefore, the surface area of the rectangular pyramid is approximately 527 cm^2.
The base area of the pyramid is given by length times width:
Base area = l * w = 13 cm * 11 cm = 143 cm^2
Now, let's calculate the area of each triangular face. Since the base of the pyramid is rectangular, the triangular faces are all congruent right triangles.
The area of a right triangle is given by (1/2) * base * height:
Triangle area = (1/2) * l * h
First, let's calculate the area of the triangle with a base of length 13 cm and height 8 cm:
Triangle area = (1/2) * 13 cm * 8 cm = 52 cm^2
Next, let's calculate the area of the triangle with a base of length 11 cm and height 8 cm:
Triangle area = (1/2) * 11 cm * 8 cm = 44 cm^2
Since the pyramid has four triangular faces, we need to multiply the area by 4 to account for all faces:
Total triangle area = 4 * (52 cm^2 + 44 cm^2) = 4 * 96 cm^2 = 384 cm^2
Finally, we can find the surface area by adding the base area and the total triangle area:
Surface area = Base area + Total triangle area = 143 cm^2 + 384 cm^2 = 527 cm^2
Therefore, the surface area of the rectangular pyramid is approximately 527 cm^2.
What s the surface area of a square pyramid with a base length of 10 cm and a slant height of 20 cm?
To find the surface area of a square pyramid, you need to calculate the area of the base and the area of the four triangular faces and add them together.
The base area of the square pyramid is given by the formula side length squared:
Base area = (side length)^2 = (10 cm)^2 = 100 cm^2
The area of each triangular face can be found using the formula (1/2) * base * height, where the base is the side length and the height is the slant height. In this case, the base and height of the triangular faces are equal in length.
Triangle area = (1/2) * base * height = (1/2) * 10 cm * 20 cm = 100 cm^2
Since the pyramid has four triangular faces, the total area of the triangular faces is equal to:
Total triangle area = 4 * Triangle area = 4 * 100 cm^2 = 400 cm^2
Now, you can find the surface area by adding the base area and the total triangular area:
Surface area = Base area + Total triangle area = 100 cm^2 + 400 cm^2 = 500 cm^2
Therefore, the surface area of the square pyramid is 500 cm^2.
The base area of the square pyramid is given by the formula side length squared:
Base area = (side length)^2 = (10 cm)^2 = 100 cm^2
The area of each triangular face can be found using the formula (1/2) * base * height, where the base is the side length and the height is the slant height. In this case, the base and height of the triangular faces are equal in length.
Triangle area = (1/2) * base * height = (1/2) * 10 cm * 20 cm = 100 cm^2
Since the pyramid has four triangular faces, the total area of the triangular faces is equal to:
Total triangle area = 4 * Triangle area = 4 * 100 cm^2 = 400 cm^2
Now, you can find the surface area by adding the base area and the total triangular area:
Surface area = Base area + Total triangle area = 100 cm^2 + 400 cm^2 = 500 cm^2
Therefore, the surface area of the square pyramid is 500 cm^2.
Use the formula for the surface area of a square pyramid to solve for the slant height if the length of the base is 40 in. and S A equals 2,800 in^2.
The formula for the surface area (SA) of a square pyramid is given by:
SA = Base area + Lateral area
The base area of a square pyramid is given by:
Base area = Base length^2
In this case, the length of the base (l) is 40 in., so the base area is:
Base area = (40 in)^2 = 1600 in^2
The lateral area of a pyramid consists of four congruent triangles. The area of each triangular face is given by:
Triangle area = (1/2) * Base length * Slant height
Let's denote the slant height as h. The lateral area is the sum of the areas of the four triangular faces:
Lateral area = 4 * (1/2) * Base length * Slant height = 2 * Base length * Slant height
Now, let's use the formula for the surface area to set up an equation:
SA = Base area + Lateral area
2800 in^2 = 1600 in^2 + 2 * 40 in * h
2800 in^2 = 1600 in^2 + 80 in * h
Subtracting 1600 in^2 from both sides of the equation gives:
1200 in^2 = 80 in * h
Dividing both sides of the equation by 80 in gives:
15 in = h
Therefore, the slant height of the square pyramid is 15 in.
SA = Base area + Lateral area
The base area of a square pyramid is given by:
Base area = Base length^2
In this case, the length of the base (l) is 40 in., so the base area is:
Base area = (40 in)^2 = 1600 in^2
The lateral area of a pyramid consists of four congruent triangles. The area of each triangular face is given by:
Triangle area = (1/2) * Base length * Slant height
Let's denote the slant height as h. The lateral area is the sum of the areas of the four triangular faces:
Lateral area = 4 * (1/2) * Base length * Slant height = 2 * Base length * Slant height
Now, let's use the formula for the surface area to set up an equation:
SA = Base area + Lateral area
2800 in^2 = 1600 in^2 + 2 * 40 in * h
2800 in^2 = 1600 in^2 + 80 in * h
Subtracting 1600 in^2 from both sides of the equation gives:
1200 in^2 = 80 in * h
Dividing both sides of the equation by 80 in gives:
15 in = h
Therefore, the slant height of the square pyramid is 15 in.