A Triangular Pyramid Has A Volume Of 180 Cubic Cm & A Height Of 12 Cm. Find The Length Of A Side Of The Triangular Base If The Triangle's Height Is 6 Cm?

FORMULA FOR THE VOLUME OF TRIANGULAR PYRAMID IS :

Volume = 1/3 × [Base Area] × Height

A triangular pyramid has has 4 Faces , The 3 Side Faces are Triangles, The Base is also a Triangle , It has 4 Vertices (corner points), It has 6 Edges
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Volume = 180 cubic cm
Height = 12 cm.

We can calculate the base area. I.e.

Base area = 3 x volume / height

= 3 x 180 / 12

= 45 cm square.

Base area = 1/ 2 x base x height

45 = 1/2 x 6 x height (height of base triangle)

45x2 / 6 = height

height = 90/6

height = 15

now we know the height and base of base triangle. I.e. 15 and 6

one of the sides of the base triangle can be calculated through pythagorean theorem.

H^2 = p^2 + b^2

h^2 = 15^2 + 3^2

h^2 = 225+9

h= 15.297 answer.

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