how do i found the volume and total surface area of the sqaure pyramid if the perpendicular high is 14.0cm :confused:

http://i10.photobucket.com/albums/a1...5/DSC01025.jpg

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- May 15th 2007, 07:17 AMturbod15bVolume & total surface area
how do i found the volume and total surface area of the sqaure pyramid if the perpendicular high is 14.0cm :confused:

http://i10.photobucket.com/albums/a1...5/DSC01025.jpg - May 15th 2007, 07:41 AMGeometor
ok, the formula to working out the VOLUME of any pyramid is:

1/3 x area of base x height (perpendicular height)

so if we substitue the numbers in...

we will have ((5 x 5) / 3) x 14

= 116.66666 (recurring) cm^3

now to find the total surface area...

that means, adding up the areas of the square base and the 4 other triangles around it

the area of the base = 5x5 = 25

the area of each triangle = (14 x 5)/2 = 35

so 4 triangles = 4 x 35 = 140

140 + 25 = 165

so total surface area = 165cm^2 - May 15th 2007, 07:42 AMJhevon
well, the manual way to do it is to just find the area of the base, which is a sqaure and add it to the area of all the sides which are triangles. you can find the height of the triangle by using Pythagoras' theorem to find the hypotenuse of triangle ABC in the diagram (i assume the vertex is labeled A).

but there are nice compact formulas for the surface area and volume of square-based pyramids. see the link below.

see Surface Area and Volume - May 15th 2007, 11:45 AMSoroban
Hello, turbod15b!

I assume that the top vertex is A.

For the surface area:

The base is a square. .Its area is: 5² = 25 cm².

In the base, triangle BCE is 45° right triangle.

Since CE = 2.5, then BC = 2.5 cm

The sides of the pyramid are four congruent triangles.

Triangle ADE has base DE = 5 and height AC.

In right triangle ABC__: AC__² = .AB² + BC² .= .14² + 2.5² .= .809/4

. . Hence: .AC = ½√809

. . . . . . . . . . . . . . . . . . . . . .___ . . . . . . . ___

The area of ∆ADE .= .½(5)(½√809) .= .¼·5√809

. . . . . . . . . . . . . . . . . . . . . . . . . .___

The area of the four triangles is: .5√809

. . - . . . - . . . . . . . . . . . . . ___

The total surface area is: .5√809 + 25 .≈ .167.2 cm²