<p>Other questions I am having difficulty with.</p>
<p>1.
A pyramid shown has an altitude (h) and a square base of side (m). The four edges that meet at (V), the vertex of the pyramid, each have length (e). If (e)=(m), what is the value of (h) in terms of (m)? </p>
<p>(A) m / square root2</p>
<p>(B) m square root2 / 2</p>
<p>(C) m</p>
<p>(D) 2m / square root3</p>
<p>(E) m square 2</p>
<hr>
<p>Don’t know how well my explanation will come across via text only.</p>
<p>Okay, so what you need to do is to mentally “slice” the pyramid along the diagonal of the square base, going through the vertex. Then draw out the triangle formed by the “slicing”</p>
<p>…/
./…
/___</p>
<p>Okay, it will look something like that. (Ignore the dots. I fail at ASCII art).</p>
<p>Oh, and I’m going to use the typical computer notation. sqrt(2) = square root of two.</p>
<p>Now, the base of this triangle is sqrt(2)*m (b/c the base of pyramid is a square) and the sides are each m. If you drop the height, then you can see that it’s a right triangle and thus (m^2)-(m/sqrt(2))^2 = height^2</p>
<p>Simplify: height^2 = m^2 - m^2/2 = m^2/2</p>
<p>Square root of that is m/sqrt(2) . Answer is A.</p>
<p>the way I did it I got B…but then I realized A and B are the same answer. (Multiply A by sqrt(2)/sqrt(2) which equals 1, and it becomes B)</p>