A metalworker is creating decorative points in the form of a 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 formulas to find the surface area of each pyramid based on the figure. L= 3.9 cm, W= 4.5 cm, H= 3.5 cm
To find the surface area of a triangular pyramid, we need to calculate the areas of each of the faces and add them together.
The formula for the surface area of a triangular pyramid is:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
Given:
L = 3.9 cm (Length of the base of the triangle)
W = 4.5 cm (Width of the base of the triangle)
H = 3.5 cm (Height of the pyramid)
First, let's find the base area of the triangular pyramid:
Base Area = (0.5 * Length of Base * Width of Base)
Base Area = (0.5 * 3.9 cm * 4.5 cm)
Base Area = 8.775 cm²
Next, let's find the slant height of the triangular pyramid.
We can use the Pythagorean theorem. The slant height (s) is the hypotenuse of a right-angled triangle with sides equal to the height (H) and half the length of the base (L/2).
s = √[(L/2)^2 + H^2]
s = √[(3.9 cm/2)^2 + 3.5 cm^2]
s = √[1.95 cm^2 + 12.25 cm^2]
s = √14.2 cm^2
s ≈ 3.77 cm
Now, let's find the perimeter of the base:
Perimeter of Base = (Length of Base + Width of Base + Hypotenuse of the right-angled triangle)
Perimeter of Base = (3.9 cm + 4.5 cm + √14.2 cm)
Perimeter of Base ≈ 11.67 cm
Finally, let's calculate the surface area of the triangular pyramid:
Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)
Surface Area = 8.775 cm² + (0.5 * 11.67 cm * 3.77 cm)
Surface Area = 8.775 cm² + (20.84 cm²)
Surface Area ≈ 29.615 cm²
Therefore, the surface area of each pyramid is approximately 29.615 cm².
what is the length of a right rectangular prism with the volume of 90 width 3 and height of 5
To find the length of a right rectangular prism with volume 90, width 3, and height 5, we can use the formula:
Volume = Length * Width * Height
Given:
Volume = 90
Width = 3
Height = 5
Substituting the given values into the formula, we have:
90 = Length * 3 * 5
To solve for the length, divide both sides of the equation by the product of the width and height:
Length = 90 / (3 * 5)
Length = 90 / 15
Length = 6
Therefore, the length of the right rectangular prism is 6 units.
prism has an area of 20 square units and a height of 3 square units what is the volume
I'm sorry, but there seems to be a mistake in your question. The area of a prism is measured in square units, not cubic units. Additionally, the height of a prism is measured in linear units, not square units.
If you have the correct values for the area and height of the prism, please provide them and I'll be happy to help you calculate the volume.
right rectangular prism
To calculate the volume of a right rectangular prism, you need to know the length, width, and height of the prism. The formula for finding the volume is:
Volume = length * width * height
Given that the area of the prism is 20 square units and the height is 3 linear units, we don't have enough information to directly calculate the volume. The area of a prism is found by adding up the individual areas of its faces, which are typically rectangular. Therefore, we need the dimensions (length and width) of the prism to proceed.