Common Core Standards: Math
9. Derive the formula A = ½ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
Area 51, originally intended to be a testing site for the U-2 spy plane, has grown in pop culture and infamy to outlandish proportions. The alleged site of myriad government and military cover-ups, this location is well known around world for its rumored possession and testing of alien technologies and specimens.
Many parents scoff at the idea that the government needs to cover up any evidence of extraterrestrial life, claiming their very own teenage offspring have clearly been replaced with aliens. We here at Shmoop are keeping our mouths shut. After all, that kind of information is classified for a reason.
As for Area 51, well, we disavow any knowledge of that topic as well.
But finding the area of a triangle is public knowledge that we are willing and able to discuss. Even young spacelings—er, students—are familiar with the topic. By second grade, they have begun their study of area by counting the number of squares inside a shape. By sixth grade, they've calculated area with formulas. And now, they need to be able to derive the formula for finding the area of a triangle.
Before they become convinced that the standard expects them to master an alien concept, have them work through a few sample problems. Start with the original formula they learned (A = ½bh) and a few right triangles. Then demonstrate the derivation of the fancier sine-based version and relate it to the simpler one.
Being able to derive the formula is one skill that will be crucial for those students choosing to enroll in more advanced math courses, like analytic geometry, applied calculus, and intergalactic algebra.