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Posted on Jan 02, 2017

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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

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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

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

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

Mar 19, 2015 | Office Equipment & Supplies

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.

We can now put the length and height into the formula to calculate the area of the triangle.

Good luck.

Paul

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.

We can now put the length and height into the formula to calculate the area of the triangle.

Good luck.

Paul

Mar 19, 2015 | Office Equipment & Supplies

Volume of right cylinder is

V=(Area of base)*height.

If cylinder is circular Area of base =PI*radius^2=Pi*r^2

Volume is**V=Pi*(8^2)*6 cm^2**

Finish the calculation.

V=(Area of base)*height.

If cylinder is circular Area of base =PI*radius^2=Pi*r^2

Volume is

Finish the calculation.

Jun 28, 2014 | Office Equipment & Supplies

Volume of right cylinder is

V=(Area of base)*height.

If cylinder is circular Area of base =PI*radius^2=Pi*r^2

Volume is**V=Pi*(8^2)*6 cm^2**

Finish the calculation.

V=(Area of base)*height.

If cylinder is circular Area of base =PI*radius^2=Pi*r^2

Volume is

Finish the calculation.

Jun 28, 2014 | Casio MS-80TE Calculator

I assume the length of a side is 16 in, and the height of the prism is 23 inches.

**Volume of a prism is V_prism=(Area of base)*(height of prism)**

Area of base is made up of the area of the 6 equilateral triangles with sides =16 inches. The height of such triangles is given by**8*SQRT(3)**.

Use the Pythagorean theorem or the trigonometric ratios to find the height of each of the 6 traingles.

Area of base =6*16*(8*SQRT(3))/2 sq in

**Volume =6*8*8*23*SQRT(3) cubic inches**

Calculate the value in cubic inches and convert to gallons: I leave that task to you.

Area of base is made up of the area of the 6 equilateral triangles with sides =16 inches. The height of such triangles is given by

Use the Pythagorean theorem or the trigonometric ratios to find the height of each of the 6 traingles.

Area of base =6*16*(8*SQRT(3))/2 sq in

Calculate the value in cubic inches and convert to gallons: I leave that task to you.

May 12, 2014 | Office Equipment & Supplies

Here is to get you started. To increase the size of the image do a CTRL Plus (+) in your browser.

You need to calculate the slant height of the pyramid for the formula of the lateral area. You should find a value of** (1/2)*SQRT(203) **or about 7.1239 cm

You need to calculate the altitude (height) of the pyramid from the apex (summit) to the center of the base triangle (center of inscribed circle, barycenter, orthocenter). The hypotenuse of such triangle is the slant height. One leg is the altitude (to be found),**the measure of the second leg is (1/3) the altitude** **of the equilateral triangle** that forms the base. You should find (1/3) m MH= (1/3)* **(11/2)*SQRT(3)**

1. Calculate the area of the base (use a formula for the equilateral triangle or the general formula for a triangle: you have its height MH ).

2. Lateral area = 3 times the area of triangle Triangle ECD (in yellow above).

3. Total area = area of base + lateral area.

4. Volume= (1/3)(Area of base)* (height of pyramid)

If you can see the details on the screen capture below, fine, Press CTRL + in your browser to increase the size.

You need to calculate the slant height of the pyramid for the formula of the lateral area. You should find a value of

You need to calculate the altitude (height) of the pyramid from the apex (summit) to the center of the base triangle (center of inscribed circle, barycenter, orthocenter). The hypotenuse of such triangle is the slant height. One leg is the altitude (to be found),

1. Calculate the area of the base (use a formula for the equilateral triangle or the general formula for a triangle: you have its height MH ).

2. Lateral area = 3 times the area of triangle Triangle ECD (in yellow above).

3. Total area = area of base + lateral area.

4. Volume= (1/3)(Area of base)* (height of pyramid)

If you can see the details on the screen capture below, fine, Press CTRL + in your browser to increase the size.

Mar 29, 2014 | Office Equipment & Supplies

The formula to find the volume of right prisms and right cylinders is

**Volume=(area of base)*height**

If the cylinder has a**circular base,** then the area of the base is PI*R^2

and the volume is Pi*(R^2)*H.

Here R is measure of the Radius, and H is the measure of the Height. R and H must be expressed in the same unit.

If the cylinder has a

and the volume is Pi*(R^2)*H.

Here R is measure of the Radius, and H is the measure of the Height. R and H must be expressed in the same unit.

Jan 26, 2014 | Texas Instruments TI-84 Plus Calculator

There isn't a single formula for solids of different shapes.
For a right solid with a rectangular base - volume is base area x height
Similarly for cylinder with a circular base - volume = base area x height (base area in this case is Pi x radius2).
For a sphere - volume = 4/3 x Pi x radius3

Jul 07, 2011 | Computers & Internet

I am sorry to say it but your units do not make sense: Units of volumes and areas are mixed up.

Let us try to make sense of it.

If you have some container whose base is 3 square meters (not cubic meter sq) and it has a height of 3 inches you can calculate its volume in cubic meters or in cubic inches or cubic feet. To do so convert the height in inches into meters and multiply the area of the base by the height in meters and you will obtain the volume in cubic meters. To get the volume in cubic inches convert the area of the base to square inches and multiply by the height in inches.

However, even after you have expressed the volume in one unit or another (m^3 or in^3) you cannot find the mass of the substance contained (be it in tons, tonnes or kilograms): You need to know the substance and more specifically its density or its specific gravity).

Please, reformulate your question and specify the substance that fills or would fill the volume. Without that information, nothing doing.

Let us try to make sense of it.

If you have some container whose base is 3 square meters (not cubic meter sq) and it has a height of 3 inches you can calculate its volume in cubic meters or in cubic inches or cubic feet. To do so convert the height in inches into meters and multiply the area of the base by the height in meters and you will obtain the volume in cubic meters. To get the volume in cubic inches convert the area of the base to square inches and multiply by the height in inches.

However, even after you have expressed the volume in one unit or another (m^3 or in^3) you cannot find the mass of the substance contained (be it in tons, tonnes or kilograms): You need to know the substance and more specifically its density or its specific gravity).

Please, reformulate your question and specify the substance that fills or would fill the volume. Without that information, nothing doing.

Apr 08, 2011 | Office Equipment & Supplies

Hello,

I will give you some hints, and indications. You do the Math.

You have a certain volume of dirt that has to be moved. For that you use a pale the volume of which you do not know right now, but can calculate.

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.

**Volume of pale **

Solid Shape? Cylinder (its base is circular)

Volume of a cylinder: Area of the circular base times the height (10inc.)

To calculate the volume I need the area of the circular base.

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.

Number of times one has to scoop.

**Number = Volume of dirt / volume of pale**

You cannot proceed further until you correct the error in the data. As you can see, when you calculate the volume of the pale the unit is cubic inches. However, your question states 5600 cubic of dirt.

Do you see what is missing?

Now you are on your own. Good sailing.

I will give you some hints, and indications. You do the Math.

You have a certain volume of dirt that has to be moved. For that you use a pale the volume of which you do not know right now, but can calculate.

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.

Solid Shape? Cylinder (its base is circular)

Volume of a cylinder: Area of the circular base times the height (10inc.)

To calculate the volume I need the area of the circular base.

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.

Number of times one has to scoop.

You cannot proceed further until you correct the error in the data. As you can see, when you calculate the volume of the pale the unit is cubic inches. However, your question states 5600 cubic of dirt.

Do you see what is missing?

Now you are on your own. Good sailing.

Nov 01, 2009 | The Learning Company Achieve! Math &...

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