Answer:
The height of the pyramid = 8 cm
Step-by-step explanation:
Given that,
The edges of a pyramid, a = 12 cm
The lateral area of a pyramid, A = 240 cm²
The formula for the lateral area of a square pyramid is given by :
[tex]A=a\sqrt{a^2+4h^2}[/tex]
Where
h is the height
Squaring both sides,
[tex]A^2=a^2\times (a^2+4h^2)\\\\\dfrac{A^2}{a^2}=a^2+4h^2\\\\\dfrac{A^2}{a^2}-a^2=4h^2\\\\4h^2=\dfrac{(240)^2}{12^2}-12^2\\\\4h^2=256\\\\h^2=64\\\\h = 8\ cm[/tex]
So, the height of the pyramid is equal to 8 cm.
