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# Quadrilateral Perimeters and Areas Help (page 2)

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## Perimeter and Area of a Trapezoid

### Perimeter Of Trapezoid

Suppose we have a trapezoid defined by points P, Q, R , and S , and having sides of lengths d, e, f , and g as shown in Fig. 3-17. Let d be the base length, let h be the height, let x be the angle between the sides having length d and e , and let y be the angle between the sides having length d and g . Suppose the sides having lengths d and f (line segments RS and PQ ) are parallel. Then the perimeter, B , of the trapezoid is:

B = d + e + f + g

Fig. 3-17 . Perimeter and area of trapezoid. Dimensions and angles are discussed in the text.

### Interior Area Of Trapezoid

Suppose we have a trapezoid as defined above and in Fig. 3-17. The interior area, A , is equal to the average (or arithmetic mean ) of the lengths of the base and the top, multiplied by the height. The formula for calculating A is as follows:

A = [( d + f )/2] h

= ( dh + fh )/2

Suppose m represents the length of the median of the trapezoid, that is, a line segment parallel to the base and the top, and midway between them. Then the interior area is equal to the product of the length of the median and the height:

A = mh

Practice problems for these concepts can be found at:  Quadrilaterals Practice Test.

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