Geometry Activities | MathHelp.com - By MathHelp.com
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| 00:0-1 | to find the area of the triangle . Shown . | |
| 00:03 | We use our formula for the area of a triangle | |
| 00:07 | , which is one half base times height . The | |
| 00:15 | base of the Triangle has a length of 24 , | |
| 00:18 | but we don't know the height . In fact , | |
| 00:21 | we don't even have a segment that represents the height | |
| 00:25 | . So let's draw one in . Yeah . And | |
| 00:33 | let's label this segment as H since it represents the | |
| 00:36 | height . Next notice that the original triangle is isosceles | |
| 00:43 | since two of its sides are congruent . So the | |
| 00:47 | segment that we've just drawn creates two congruent right triangles | |
| 00:53 | . Bye hi pot noose leg . Therefore it divides | |
| 00:58 | the base which has a length of 24 Into two | |
| 01:02 | congruent segments each with a length of 12 . Now | |
| 01:10 | , if we use the right triangle on the right | |
| 01:13 | side of the figure , we can find the value | |
| 01:16 | of H . Using the pythagorean theorem . And we | |
| 01:21 | have aged squared plus 12 squared equals 20 squared . | |
| 01:28 | Yeah , mm Solving from here , 12 squared is | |
| 01:40 | 144 and 20 squared is 400 . So we have | |
| 01:47 | aged squared Plus 144 equals 400 . subtracting 144 from | |
| 01:57 | both sides gives us a chance squared Equals 256 . | |
| 02:08 | And square rooting both sides , We find that h | |
| 02:13 | equals 16 Mhm . Which means that we can replace | |
| 02:19 | the H&R Diagram with a 16 . So the area | |
| 02:29 | of the original triangle , Which is 1/2 base times | |
| 02:34 | height Is 1/2 times 24 times 16 . Yeah . | |
| 02:41 | Yes . Yeah 24 times 16 is 384 . So | |
| 02:55 | we have one half times 384 Which equals 192 . | |
| 03:06 | So the area of the original triangle shown is 192 | |
| 00:0-1 | . |
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