# quadrilateral area and diagonals

7. Figure 4 shows a survey of a building which forms a quadrilateral ABCD

Calculate a) the length of the diagonals - AC and BD

b) the area of the plot ABCD

Please see attachment for diagrams.

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#### Solution Preview

7.a

AC^2 = AB^2 + BC^2 - 2*AB*BC*cos(65)

=> AC = sqrt(21.4^2 + 29.6^2 - 2*21.4*29.6*cos(65)) = 28.26 --ANSWER

To estimate BD:

AC^2 = AD^2 + DC^2 - 2 * AD * DC * cos(ADC) = AB^2 + BC^2 - 2*AB*BC*cos(65)

=> 2*AD*DC*cos(ADC) = AD^2 + DC^2 - AB^2 - BC^2 ...

#### Solution Summary

Estimation of length of diagonals of a quadrilateral and area of the quadrilateral is given in the solution.

$2.19