Answer:
S = S(ABCD) - S(BCE) - S(AED) = 7*6 - 2*6/2 - 5*6/2 = 42 - 6 - 15 = 21
Step-by-step explanation:
If we look at the picture, we can notice that the area we are interested in is S(ABCD) - S(BCE) - S(AED). Y-axis is parallel to AB line since the coordinates of the A and B points have the same X-axis value.
The following calculations happend for figuring out the width for each line:
- AB = | -3 - 4 | = 7
- BC = | -4 - 2 | = 6
- CE = | 4 - 2 | = 2
- ED = | 2 - (-3) | = 5
- AD = | -4 - 2 | = 6
The formulas for each figure area:
- S(ABCD) = AB * BC
- S(BCE) = BC * CE / 2
- S(AED) = ED * AD / 2
