+118725 http://easycalculation.com/maths-dictionary/lateral_area.html
There were a couple of different definitions. It was a bit confusing.
I think for prism you don't include the two ends and for pyramids you don't include the bottom.
I don't think i have heard the term lateral surface area before.
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Now I will look at the first one.
The top and bottom are right angled triangles. They are the same. The sides are 6,8 and 10km
so the area is 2 * (1/2 * 6 * 8) = 2*(24) = 48km2
The other 3 sides are rectangles the total area is (4*6)+(4*8)+(4*10) = 24+32+40=96km2
Total area = 48+96 = 144km2
Lateral area = 96km2
+118725 $$x^2-4x-2^x=0$$
$$As\:\:x\rightarrow+\inf \:\:(x^2-4x-2^x)\rightarrow-\inf\\
As\:\:x\rightarrow-\inf \:\:(x^2-4x-2^x)\rightarrow+\inf$$
Therefore there must be an odd number of roots. I'm going to look for just 1
Finding the root of this is not super easy. It can't be factorised.
Let's consider $$f(x)x^2-4x-2^x$$
first I notice that as
$$If \:\: x=0 \mbox{ then } f(x)=0-0-1=-1$$
$$If \:\: x=-1 \mbox{ then } f(x)=1+4-1/2=+4.5$$
So there is at least one root between x=-1 ans x=0
Now use Newton's method of approximating roots to find it.
http://en.wikipedia.org/wiki/Newton's_method
There are you tube videos covering this as well. If you google them.
This is what the graph looks like
+118725 That's fabulous. Thank you Lucifer van Pelt. ROF LOL
**It might also be the case for me, for answers and solutions so near to perfection that only small atoms can slip into the “cracks of its imperfections."** Tickets please! 
Reference for "to-ma-to," "to-mah-to”
http://web2.0calc.com/questions/expressions_2#r103393
See you next time! 
The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, approximately equal to 3.14159. It has been represented by the Greek letter "π" since the mid-18th century though it is also sometimes spelled out as "pi" (/paɪ/).
Being an irrational number, π cannot be expressed exactly as a common fraction, although fractions such as 22/7 and other rational numbers are commonly used to approximate π. Consequently its decimal representation never ends and never settles into a permanent repeating pattern. The digits appear to be randomly distributed although no proof of this has yet been discovered. Also, πis a transcendental number – a number that is not the root of any nonzero polynomial having rational coefficients. Thistranscendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straight-edge.
For thousands of years mathematicians have attempted to extend their understanding of π, sometimes by computing its value to a high degree of accuracy. Before the 15th century mathematicians such as Archimedes and Liu Hui used geometrical techniques, based on polygons, to estimate the value of π. Starting around the 15th century, new algorithms based on infinite seriesrevolutionized the computation of π. In the 20th and 21st centuries mathematicians and computer scientists discovered new approaches that, when combined with increasing computational power, extended the decimal representation of π to, as of late 2011, over 10 trillion (1013) digits.[1] Scientific applications generally require no more than 40 digits of π so the primary motivation for these computations is the human desire to break records but the extensive calculations involved have been used to test supercomputersand high-precision multiplication algorithms.
Because its definition relates to the circle, π is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses or spheres. It is also found in formulae used in other branches of science such as cosmology, number theory,statistics, fractals, thermodynamics, mechanics and electromagnetism. The ubiquity of π makes it one of the most widely-known mathematical constants both inside and outside the scientific community: Several books devoted to it have been published, the number is celebrated on Pi Day and record-setting calculations of the digits of π often result in news headlines. Attempts to memorize the value of π with increasing precision have led to records of over 67,000 digits. -Wikipedia
