Name: Surface Area and Volume of Right Triangular Pyramid
Uploaded: 2019-07-19
Duration: 3 min 52 s
Description: To find the volume of a right triangular pyramid, we use the formula V = (1/3)AH, where A = area of the pyramid's base and H = height of the pyramid. Watch a...

Question

A square pyramid is to be made with the triangles shown here as a lateral face. What I would be its height?

What if the base edge is $40$ centimetres instead of $30$ centimetres?

Accepted Answer

Here, $a$ be the edge and $40$ be the height and $30$ be the slant edge of the square pyramid.

Given,

From the above:

$l^{2} = e^{2} - {(\frac{a}{2})}^{2}$

$\Rightarrow l = \sqrt{25^{2} - {(\frac{30}{2})}^{2}}$

$\Rightarrow l = \sqrt{25^{2} - 15^{2}}$

$\Rightarrow l = \sqrt{625 - 225}$

$\Rightarrow l = \sqrt{400} = 20$

We know that, $l^{2} = h^{2} + {(\frac{a}{2})}^{2}$

$\Rightarrow h = \sqrt{l^{2} - {(\frac{a}{2})}^{2}}$

$\Rightarrow h = \sqrt{20^{2} - 15^{2}}$

$\Rightarrow h = \sqrt{400 - 225}$

$\Rightarrow h = \sqrt{175} = 13.2$

So, height of the pyramid is $13.2 cm$ .

Now, base edge is $40$ centimetres.

$l^{2} = e^{2} - {(\frac{a}{2})}^{2}$

$\Rightarrow l = \sqrt{25^{2} - {(\frac{40}{2})}^{2}}$

$\Rightarrow l = \sqrt{25^{2} - 20^{2}}$

$\Rightarrow l = \sqrt{625 - 400}$

$\Rightarrow l = \sqrt{225} = 15$

We know that, $l^{2} = h^{2} + {(\frac{a}{2})}^{2}$

$\Rightarrow h = \sqrt{l^{2} - {(\frac{a}{2})}^{2}}$

$\Rightarrow h = \sqrt{15^{2} - 15^{2}}$

$\Rightarrow h = 0$

So, height of the pyramid is $0 cm$ .

A square pyramid is to be made with the triangles shown here as a lateral face. What I would be its height?

What if the base edge is $40$ centimetres instead of $30$ centimetres?

Important Questions on Solids

Learn and Prepare for any exam you want !

A square pyramid is to be made with the triangles shown here as a lateral face. What I would be its height? What if the base edge is 40 centimetres instead of 30 centimetres?

Important Questions on Solids

Learn and Prepare for any exam you want !

A square pyramid is to be made with the triangles shown here as a lateral face. What I would be its height?

What if the base edge is $40$ centimetres instead of $30$ centimetres?