Question 1125740
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The area of the square base is 100.<br>
The base of each triangular face is 10; if the area of each triangular face is equal to the area of the base of the pyramid (100), then the altitude, a, of each triangular face can be calculated from the formula for the area of a triangle:<br>
{{{100 = (1/2)(10)(a)}}}<br>
So the altitude of each triangular face is 20.<br>
Each of those altitudes, along with the height of the pyramid and half the width of the square base, forms a right triangle, with the altitude of the triangle as the hypotenuse.  Then the height of the pyramid is given by the Pythagorean Theorem:<br>
{{{h = sqrt(20^2-5^2) = sqrt(375) = 5*sqrt(15)}}}<br>
The height of the pyramid is 5*sqrt(15) meters.