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TSI Math: Solving for a Triangle's Area Using the Pythagorean Theorem 13 Views


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Description:

An isosceles triangle has legs 10 units long and a base 12 units long. What is its area in square units?


Transcript

00:02

All right sy mash my uppers next up and i

00:04

saw seles Triangle has legs thes things Ten units long

00:09

in a base Twelve units long What is its area

00:12

in square units All right Well let's See No reason

00:18

if you're triangles When in doubt draw a diagram The

00:21

area the triangles one half the base times the height

00:24

In this situation we need to find height Well if

00:26

we imagine cutting the given triangle in half to form

00:29

two right triangles like this one here the height is

00:32

the vertical leg of each right triangle Well the horizontal

00:36

leg of each right triangle is half the base of

00:39

the original triangle Because of the whole cutting in half

00:42

thing they're so here check it out Looks like this

00:44

Get the ten thing in the ten thing in the

00:46

six there in the h there which is right Well

00:48

we'll use the pythagorean theorem to find age And yes

00:51

it was his best serum by far So we've got

00:54

a squared plus b squared c squared or six squared

00:56

Plus h squared is ten square Now simplify it That

00:59

gives us thirty six Plus h squared is one hundred

01:02

subtract thirty six from both sides We get sixty for

01:06

eight square to sixty four square to sixty four is

01:09

eight So the triangle is eight units tall in the

01:12

area of the original triangle then is one half base

01:16

times height right So it's a halftime twelve times eh

01:19

which is six times eight or forty eight square units

01:23

and note that we use the full base of the

01:25

original triangle there Twelve So that's it The answer is 00:01:29.552 --> [endTime] c forty eight or shmoop Uh

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