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# What is the area of the composite figure whose vertices have the following coordinates? (-2, -2), (4, -2), (5, 1) , (2, 3)

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What is the area of the composite figure whose vertices have the following coordinates? (-2, -2), (4, -2), (5, 1) , (2, 3)

Jan 31, 2019

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$$\text{Let }A(-2,-2),B(4,-2),C(5,1),D(2,3)$$.

Connect BD.

It is obvious that $$\text{Area of }\triangle ABD = \dfrac{6\cdot 5}{2} = 15 \text{ unit}^2$$.

Now add point E(5, 3), F(2, -2), G(5, -2) on the same coordinate system.

Consider rectangle DEFG.

$$\text{Area of }\triangle BCD = \text{Area of rectangle } DEFG - \text{Area of }\triangle DEC - \text{Area of }\triangle CBG - \text{Area of }\triangle DFB$$

$$\text{Area of }\triangle BCD = 3\cdot 5 - \dfrac{2\cdot 5 + 3\cdot 2+1\cdot 3}{2} = 15 - \dfrac{19}{2}=\dfrac{11}{2} \text{ unit}^2$$.

Therefore the total area of the figure is 15 + 11/2 = 20.5 unit2.

Feb 1, 2019