Question
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 calculate the area of each individual face and then add them together.
The rectangular pyramid has a base that is a rectangle with dimensions l = 15 m and w = 12 m. The formula for the area of a rectangle is A = l * w. So, the area of the base is 15 m * 12 m = 180 m^2.
The other faces of the pyramid are triangles. To find the area of a triangle, we use the formula A = (1/2) * b * h, where b is the base and h is the height.
We have 4 triangular faces. Two of them have a base of 15 m and a height of 10 m, and the other two have a base of 12 m and a height of 10 m.
Area of the first triangular face = (1/2) * 15 m * 10 m = 75 m^2
Area of the second triangular face = (1/2) * 15 m * 10 m = 75 m^2
Area of the third triangular face = (1/2) * 12 m * 10 m = 60 m^2
Area of the fourth triangular face = (1/2) * 12 m * 10 m = 60 m^2
Now, we can add up the areas of all the faces:
180 m^2 (base) + 75 m^2 + 75 m^2 + 60 m^2 + 60 m^2 = 450 m^2
Therefore, the surface area of the rectangular pyramid is 450 m^2.
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 calculate the area of each individual face and then add them together.
The square pyramid has a base that is a square with an edge length of 1.5 cm. The formula for the area of a square is A = (side length)^2. So, the area of the base is (1.5 cm)^2 = 2.25 cm^2.
The other faces of the pyramid are triangles. To find the area of a triangle, we use the formula A = (1/2) * b * h, where b is the base (which is the same as the edge length of the square base) and h is the height (which is the slant height of the pyramid).
We have 4 triangular faces. Each of them has a base of 1.5 cm and a height of 4 cm.
Area of each triangular face = (1/2) * 1.5 cm * 4 cm = 3 cm^2
Now, we can add up the areas of all the faces:
2.25 cm^2 (base) + 3 cm^2 + 3 cm^2 + 3 cm^2 + 3 cm^2 = 14.25 cm^2
Therefore, the surface area of the square pyramid is 14.25 cm^2.
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
9.3 ft.
9.3 ft.
57.3 ft.
57.3 ft.
372 ft.
372 ft.
6.5 ft.
To find the height of the base of the triangular pyramid, we can use the formula for the surface area of a pyramid:
Surface Area = (base area) + (0.5 * perimeter * slant height)
We are given that the surface area is 100 ft^2, the base edge length is 6 ft, and the slant height is 8 ft.
Let's first find the base area:
Base Area = (base edge length)^2 = 6 ft * 6 ft = 36 ft^2
Now let's use the surface area formula:
100 ft^2 = 36 ft^2 + (0.5 * perimeter * 8 ft)
To find the perimeter, we need to find the length of one side of the triangle. For a regular triangular pyramid, all sides have the same length. We can use the Pythagorean theorem to find the length of each side. Let's call it "s".
In a right triangle formed by the base, height, and slant height, the height is the leg, the base is the other leg, and the slant height is the hypotenuse.
Using the Pythagorean theorem:
s^2 + (base/2)^2 = slant height^2
s^2 + (3 ft)^2 = 8 ft^2
s^2 + 9 ft^2 = 64 ft^2
s^2 = 55 ft^2
s ≈ √55 ft ≈ 7.42 ft
Now we can find the perimeter:
Perimeter = 3 * s = 3 * 7.42 ft ≈ 22.26 ft
Let's substitute the values into the surface area formula again:
100 ft^2 = 36 ft^2 + (0.5 * 22.26 ft * 8 ft)
100 ft^2 = 36 ft^2 + 88.96 ft^2
100 ft^2 = 124.96 ft^2
To solve for the height of the base, subtract the base edge length from the slant height:
Height of the Base = slant height - base edge length
Height of the Base = 8 ft - 6 ft = 2 ft
Therefore, the height of the base of the triangular pyramid is 2 ft.
Use the image to answer the question.
An illustration shows a 3 D triangular prism. The side of the base is 4.5 centimeters. The perpendicular height of the triangular base is 3.9 centimeters. The perpendicular height of the lateral face from the apex to the center of the base is 3.5 centimeters. There are two right angle symbols to show the perpendicular lines. The heights are shown as dashed lines.
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)
cm2
In order to calculate the surface area of the triangular pyramid, we need to calculate the area of each individual face and then add them together.
The triangular pyramid has a base that is an equilateral triangle with a side length of 4.5 cm.
The formula for the area of an equilateral triangle is A = (sqrt(3)/4) * (side length)^2. So, the area of the base is (sqrt(3)/4) * (4.5 cm)^2.
The other faces of the pyramid are triangles as well. To find the area of a triangle, we use the formula A = (1/2) * base * height.
The first triangular face has a base of 4.5 cm and a height of 3.9 cm.
Area of the first triangular face = (1/2) * 4.5 cm * 3.9 cm.
The second triangular face has a base of 4.5 cm and a height of 3.5 cm.
Area of the second triangular face = (1/2) * 4.5 cm * 3.5 cm.
Now, we can add up the areas of all the faces:
Area of base + Area of first triangular face + Area of second triangular face.
Area of base = (sqrt(3)/4) * (4.5 cm)^2.
Area of first triangular face = (1/2) * 4.5 cm * 3.9 cm.
Area of the second triangular face = (1/2) * 4.5 cm * 3.5 cm.
By simplifying the expressions and performing the calculations, we can find the surface area of the triangular pyramid.
Therefore, the surface area of each pyramid is the sum of all the areas calculated:
Area of base + Area of first triangular face + Area of second triangular face.
What is the length of a right rectangular prism with a volume of 90, width of 3, and height of 5?(1 point)
$$
To find the length of a right rectangular prism, we can use the formula for volume:
Volume = length * width * height
We are given that the volume is 90, the width is 3, and the height is 5.
Let's substitute the given values into the volume formula:
90 = length * 3 * 5
Now we can solve for the length:
length = 90 / (3 * 5)
length = 6
Therefore, the length of the right rectangular prism is 6.
A right rectangular prism has an area of 20 square units and a height of 3 units. What is the volume?(1 point)
units cubed