The lateral area for the pyramid with the equilateral base is 144 square units
Solution:
The given pyramid has 3 lateral triangular side
The figure is attached below
Base of triangle = 12 unit
Find the perpendicular
By Pythagoras theorem
[tex]hypotenuse^2 = opposite^2 + adjacent^2[/tex]
Therefore,
[tex]opposite^2 = 10^2 - 6^2\\\\opposite^2 = 100 - 36\\\\opposite^2 = 64\\\\opposite = 8[/tex]
Find the lateral surface area of 1 triangle
[tex]\text{ Area of 1 lateral triangle } = \frac{1}{2} \times opposite \times base[/tex]
[tex]\text{ Area of 1 lateral triangle } = \frac{1}{2} \times 8 \times 12\\\\\text{ Area of 1 lateral triangle } = 48[/tex]
Thus, lateral surface area of 3 triangle is:
3 x 48 = 144
Thus lateral area for the pyramid with the equilateral base is 144 square units
