anonymous
  • anonymous
Find the volume using the shaded base.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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anonymous
  • anonymous
isnt it just use the numbers 12 4 and 13 as ur 3 sides
anonymous
  • anonymous
That shape is a triangular pyramid. Triangle with sides of 3, 4 and 5 cm is the base. Height of the pyramid is 12. Volume of a pyramid is equal to \[\frac{ 1 }{ 3 }*A*h\] where A is the base area and h is the height. So A = 3*4/2 = 6 and height = 12. So V = 1/3*6*12 = 24

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anonymous
  • anonymous
how do u find the volume using the shaded base though?
anonymous
  • anonymous
i used the formula A=1/2bh=1/2(12)(4)= 24 cm^2. V=Bh= (24)(3)= 72cm^2
anonymous
  • anonymous
*V=72cm^3
anonymous
  • anonymous
Your calculation is right for a triangular prism. But that shape is a triangular pyramid.
anonymous
  • anonymous
ahh i see. But what is the area of the shaded base?
anonymous
  • anonymous
Don't look at the shaded region. Its irrelevant. Base is the triangle with sides of 3,4 and 5 cm and the height is 12 cm. You don't need other things.
anonymous
  • anonymous
Also there is a relation between a triangular prisms volume and a triangular pyramid. Pyramid's volume is one third of the prism's volume. If they have same base area and height. So volume is 72/3 = 24 again
anonymous
  • anonymous
yeah i know but the next question after this is ... T or F... The same volume can be found using the 3,4,5 triangle as the base and a 12 cm height.
anonymous
  • anonymous
I worded the question wrong.
mathstudent55
  • mathstudent55
The pyramid has a base that is a triangle with trianlge base of 12 cm and a triangle height of 4 cm. You can find the area of the base with he formula of the area of a triangle. Then the pyramid has a height of 3 cm. Use the formula for the volume of a pyramid using the area of the base found above and the height of the pyramid.
anonymous
  • anonymous
So A=24cm^2 and V=24cm^3?
mathstudent55
  • mathstudent55
\( \Large{A_{triangle} = \dfrac{bh}{2} }\) \( \Large {V_{pyramid} = \dfrac{1}{3}Bh }\), where B = area of the base, and h = height of the pyramid.
mathstudent55
  • mathstudent55
For the base, A = 12 cm * 4 cm / 2 = 24 cm^2 For the pyramid, V = (1/3)(24 cm^2)( 3 cm) = 24 cm^3 You are correct.
anonymous
  • anonymous
changed my name to peoplesay1214 so i have one more question by the way.... true or false... the height of the pyramid using the 5,12,13 base is 2.4 cm.

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