Area Formulas, a la Shmoop. Good evening. . .[Woman scientist appears in a lab] . . . I’m just whipping up a batch of some

of my favorite formulas. Please…join me. It’s so hard to pick a favorite, but I am

kind of partial to this one… the formula for the area of a circle. The magic formula? Pi times radius squared… Pi…that funky-looking number that starts

with 3.14…is a mathematical constant that tells us the ratio of the circumference of

any circle to its diameter. [Pi definition] So…the length of a circle’s radius…will

always determine the circle’s area. The bigger the radius, the bigger the area. [Circle grows larger] Then again, sometimes I’ve got a hankering

for the formula of a triangle. One-half the length of the base…

times the triangle’s height. [Area of a triangle formula] The clean lines and depth of flavor make this

little fella a real stand-out. . . [Hand takes a slice of pizza] . . .and often makes an

appearance when I’m entertaining. For example, if I’ve got a triangle with

a base length of 8 and a height of 10… The area will be 40…one-half

of 8 is 4…times 10 is 40. [Girl scientist holding a slice of pizza] At other times…I’m totally in the mood

for the parallelogram area formula. So simple, so elegant… just base times height.

When I buy paint for the lab. . . . . . or order carpet for my bedroom. . . [Woman scientist holding carpet in a bedroom] …it’s always my go-to. Got a rectangular room

that’s twelve feet by ten feet? Just multiply ‘em together to get 120 square feet… and now you know exactly how much carpet to get. [Woman scientist carpeting her bedroom floor] Oh! I plum near forgot about the trapezoid formula! So beautifully and infuriatingly complex… One-half times the sum of base one

plus base two…times the height. So…this podium, for instance. The larger base is 3 feet, the smaller base

2 feet…and the height is 4 feet. [A podium] And we get an area of 12 square feet. Oh, my babies. I couldn’t possibly pick a favorite. [Woman scientist with a variety of shapes] It would be like asking Lady Gaga to pick

her favorite song. I’d rather be caught wearing a meat dress

than be without any of you…[woman scientist wearing a meat dress]