Find the volume of an oblique triangle prism whose base is an equilateral triangle whose side is 12cm. The lateral edge of the prism is equal to the side of the base and inclined to the base plane at angle of 30 degrees.
Hello, reiward!
Find the volume of an oblique triangular prism
whose base is an equilateral triangle with side 12 cm.
The lateral edge of the prism is also 12 cm,
and is inclined to the base at an angle of 30°.
The volume of a pyramid is: .$\displaystyle V \;=\;\tfrac{1}{3}Bh$
. . where: .$\displaystyle B$ = area of base, and $\displaystyle h$ = height.
The area of an equilateral triangle of side $\displaystyle s$ is: .$\displaystyle A \:=\:\frac{\sqrt{3}}{4}s^2$
. . Hence, our pyramid has base area: .$\displaystyle B \;=\;\frac{\sqrt{3}}{4}(12^2) \;=\;36\sqrt{3}\text{ cm}^2$
Look at a cross-section of the pyramid.Code:* *| * * | * * | * 12 * |h * * | * * | * * | 30° * * * * * * * * * *
And we see that: .$\displaystyle h \,=\,6\text{ cm}$
Therefore: .$\displaystyle V \;=\;\frac{1}{3}(36\sqrt{3})(6) \;=\;72\sqrt{3}\text{ cm}^3$
Hello since we i have the same question, i thought I should post it in here too.
The problem is the same, but since we discuss prisms first, and later pyramids, i am not allowed to use that formula. The book says that the volume is the the product of the (right section x lateral edge).
The problem is, when i get the right section, i end up with a right section triangle with sides 6,6,12 (which doesn't exist). Can you help me somehow to analyze and idealized the proper way to get the right section?
My imagination tells me that when i do a sidesway on a right triangular prism on a vertex, the right section would retain one side and the other two side would have a 12sin30 or 12cos60 which is 6. Thanks in advanced.