The area of a triangle is given by: `frac(1)(2)bh`

where `b` is the distance along the base of the triangle, and `h` is the *vertical* height of the triangle.

*You do not need to know this, but this is why it works:*

Copy the triangle, and rotate and place it to form a parallelogram.

The area of a parallelogram = base x vertical height.

The area of a triangle is half of that.

What is the area of this triangle?

Area of a triangle | `= frac(1)(2)bh` |

`= frac(1)(2) xx 10 xx 8` | |

`= 40 cm^2` |

Answer: 40cm^{2}

A triangle is twice as high as it is wide. If the area of the triangle is 32 cm^{2}, what is the height of the triangle?

Area of Triangle | = base x height | |

Let the base be `x`: | `h` | `= 2x` |

Substitute: | 32 | `= x xx 2x` |

32 | `= 2x^2` | |

Divide both sides by 2: | 16 | `= x^2` |

Square root both sides: | 4 | `= x` |

Answer: 4 cm

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