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

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

Geometry and Measurement | Measurement (Linear, Area, Three-Dimensional) |

Mathematics and Statistics Assessment | Measurement (Linear, Area, Three-Dimensional) |

Product Type | TSI |

TSI | Mathematics and Statistics Assessment TSI Math TSI Mathematics |

TSI Math | Geometry and Measurement |

TSI Mathematics | Geometry and Measurement |

Test Prep | TSI |

### Transcript

area the triangles one half the base times the height

In this situation we need to find height Well if

we imagine cutting the given triangle in half to form

two right triangles like this one here the height is

the vertical leg of each right triangle Well the horizontal

leg of each right triangle is half the base of

the original triangle Because of the whole cutting in half

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

Get the ten thing in the ten thing in the

six there in the h there which is right Well

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

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

a squared plus b squared c squared or six squared

Plus h squared is ten square Now simplify it That

gives us thirty six Plus h squared is one hundred

subtract thirty six from both sides We get sixty for

eight square to sixty four square to sixty four is

eight So the triangle is eight units tall in the

area of the original triangle then is one half base

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

which is six times eight or forty eight square units

and note that we use the full base of the

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