# What is the volume when the base area is 56in2, height 6

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Posted on Jan 02, 2017

Use the formula for the area of the triangle Area=b*h/2.
If the base becomes b'=2b and h'=h/2, then the area of this new triangle is Area'= (2b)*(h/2)/2.
As you can see the two 2's introduced cancel one another and the area is unchanged. A'=A.

If the base is doubled and the height remains the same, then b''=2b, and h''=h. Substitute in the area formula for a triangle to get
A''=b''*h''/2= (2b)*h/2= 2*(b*h/2)=2A
You see that in this case the area is doubled.

Posted on Jan 22, 2012

Use the formula for the area of the triangle with symbols.
Let b be the measure of the base, and h the measure of the height.
The area of the triangle is A= b*h/2 (original situation)
Now consider the new situation (situation2)
Let b` the new base and h`the new height.
We have b'=2b, and h`=h/2
The new area A`=b`*h`/2=(2b)*(h/2)/2=b*h/2 and that is equal to the original situation.
Now consider a third situation
Let b"=2b, h"=h
A"=b"*h"/2=(2b)*h/2=2(b*h/2)=2A

Posted on Mar 11, 2012

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I find the easiest way to solve these is to sketch them first (I'm a visual learner;) We get a nice right-angled triangle, with the right-angle at B. The formula for the area of a triangle is 1/2 * base* height or (base * height)/2.

We can use BC or AB as the base.

If we use BC as the base, the length is 9-4 or 5. The height is 6-2 or 4.

We can now but the base and the height in the formula to figure out the area.

Good luck.

Paul

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The area of a triangle is 1/2 times base times height. A sketch of the triangle in the coordinate plane will determine how easy or hard this will be to be. From the sketch, you will see that this is a right-angled triangle with B being the right-angle. This makes it easier because we can easily determine the base and the height to use in the formula.

We can chose AB or BC to be the base, while the other will be the height. If we choose the base of AB, its length is 4, the 6 - 2. The height is 9-(-4) or 13.

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Here is to get you started. To increase the size of the image do a CTRL Plus (+) in your browser.
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If you can see the details on the screen capture below, fine, Press CTRL + in your browser to increase the size.

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Hello,
I will give you some hints, and indications. You do the Math.
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The final question is: How many time do you have to scoop with the pale to move the volume of dirt.

Answer: The number of times I have to fill the pale is equal to the Total volume of dirt divided by the as yet unknown volume of the pale.

As you can see we cannot proceed further until we find the volume of the pale.

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Volume of a cylinder: Area of the circular base times the height (10inc.)
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Area of the base =Pi* square of radius = Pi *(6)^2 in^2 (do not forget the units)

Volume of pale = Pi* (6^2)*10 in^2 * in =Pi*10*6^2 cubic inches.

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