The area of a **trapezium** is `A = frac(1)(2)(a + b)h`.

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

Fit two trapezia together, side by side, to make a parallelogram. One of the parallelograms needs to be flipped.

The area of a parallelogram is base x perpendicular height. For this parallelogram, `text(area) = (a + b) xx height`.

The parallelogram is equal to two trapezia, therefore the area of one trapezium is `A = frac(1)(2)(a + b)h`

What is the area of the trapezium, shown below?

Area of Trapezium | = `frac(1)(2)`(a + b) x h | |

Substitute | `A` | `= frac(1)(2)(14 + 20) xx 10` |

Divide both sides by 20 | `A` | `= 170` |

Answer: 170 cm^{2}

The parallel sides of a trapezium are 18 and 22 cm long. The area of the trapezium is 400 cm^{2}. What is the perpendicular height of the trapezium?

Area of Trapezium | = `frac(1)(2)`(a + b) x h | |

Substitute | `400` | `= frac(1)(2)(18 + 22)h` |

400 | `= 20h` | |

Divide both sides by 20 | 20 | `= h` |

Answer: 2.2 cm

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