An oblique triangular pyramid has a base area of 21 square units and a volume of 35 cubic units. What is the height of the pyramid?
units
Find the volume of the triangular pyramid given the measures shown. Note that the figure is not to scale. Enter your answer as a fraction.
Draw
To find the height of the oblique triangular pyramid, you can use the formula for the volume of a pyramid:
[
V = frac{1}{3} times text{Base Area} times text{Height}
]
Where:
– ( V ) is the volume,
– Base Area is the area of the base,
– Height is the height of the pyramid.
Given:
– Volume (( V )) = 35 cubic units,
– Base Area = 21 square units.
Now, plug in the values:
[
35 = frac{1}{3} times 21 times text{Height}
]
To isolate Height, first multiply both sides by 3:
[
105 = 21 times text{Height}
]
Now, divide both sides by 21:
[
text{Height} = frac{105}{21} = 5
]
So, the height of the pyramid is:
5 units.
You can always refer to additional resources for further understanding. Let me know if you have more questions!
To find the height of an oblique triangular pyramid, you can use the formula for the volume of a pyramid:
[
V = frac{1}{3} times text{Base Area} times text{Height}
]
Given:
– Volume (V = 35) cubic units
– Base Area = 21 square units
You can rearrange the formula to find the height:
[
text{Height} = frac{3V}{text{Base Area}}
]
Now plug in the values:
[
text{Height} = frac{3 times 35}{21} = frac{105}{21} = 5 text{ units}
]
So, the height of the pyramid is 5 units. If you have further questions or need more assistance, feel free to ask!