Question

Figure below shows the diagram drawn on a square sheet of paper for constructing a square pyramid.
What is the length of a side of the square sheet of paper taken?
The figure drawn in the square paper is cut out and folded to make a square pyramid.
What would be the height of that pyramid?

Answer 1

$L$ is the midpoint of $AB$

Hence $AL=BL=6m$

In right-angled triangle $△PLB,$

$P{B}^2=P{L}^2+B{L}^2$

$\Rightarrow P{L}^2=P{B}^2-B{L}^2$

$\Rightarrow P{L}^2=(10{)}^2-(6{)}^2$

$=100-36=64$

$\Rightarrow PL=8m$

Now, we know that the sides of similar triangles are equal i.e., $PL=NR=8m$

Since $ABCD$ is a square, $AB=BC=CD=AD=12m$

$\Rightarrow LN=12m$

Now, length of side of square $=PL+LN+NR$

$=8+12+8=28m$

Let $h$ be the height of the pyramid
Then $h=\sqrt{l^2-r^2}$

$\Rightarrow h=\sqrt{8^2-6^2}$

$=\sqrt{64-36}$

$=\sqrt{28}$

$=2\sqrt{7}cm$