Is wikipedia formula wrong? It is known that Heron solved an equation using the positive value of a negative squareroot.
Wikipedia says it was the volume of a frustum, The alternative formula is therefore
${\displaystyle V={\frac {h}{3}}(B_{1}+{\sqrt {B_{1}B_{2}}}+B_{2})} V = \frac{h}{3}(B_1+\sqrt{B_1 B_2}+B_2) {(1)}$
Heron of Alexandria is noted for deriving this formula and with it encountering the imaginary number, the square root of negative one
but the source quoted for this info indicates the formula of the height of a frustum knowing its slant c ($h=\sqrt{c^2- \2((a-b)/2)^2}$,(2) when c = 15 a=28 and b=4.
I don't see how the first formula can give a negative and believe the second is wrong since the the figure in red is clearly out of place.
Can you say what is the truth and what is the actual recorded formula thad Heron solved ignoring the negative signe of the squareroot?
 A: The formula
$$h=\sqrt{c^2-2\left(a-b\over2\right)^2}$$
is correct, but you need to know what the variable $c$ stands for.  It is the length of the edge connecting a corner of the (large) bottom square of side length $a$ to the nearest corner of the (small) top square of side length $b$, where the top square is centered above the bottom square.  It's this formula that gives the square root of a negative number for $(a,b,c)=(28,4,15)$.  All that's going on, really, is that there cannot be a pyramidal frustum with those measurements: If the top and bottom squares have side lengths $4$ and $28$, the slanted edge length $c$ must be greater than $\sqrt{288}\approx17$.  
To be clear, 
$$d=\sqrt2\left(a-b\over2\right)$$
is the length of the diagonal connecting a corner of the bottom square with a corner of the projection of the (centered) top square to the plane of the bottom square, so that $d$ and $h$ are the sides of a right triangle with hypotenuse $c$.  
Remarks: The formula for $h$ does not appear in the linked-to Wikipedia article; there is only an allusion there to a connection with imaginary numbers, and a reference to Paul Nahin's book, An Imaginary Tale: The Story of $\sqrt{-1}$.  The formula appears in Nahin's book in the Introduction, on page 4, along with a complete story of Heron's "near miss" of imaginary numbers. (Short version: Heron, or a later copyist, computed $15^2-2\cdot12^2=-63$, ignored the minus sign, and decided $h=\sqrt{63}$ was the height of the (non-existent!) frustum.)
