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Question

Find the area and match the pair.

A
47.5 square units
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B
72 square units
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C
10.5 square units
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Solution

Area of the triangle with coordinates (x1,y1),(x2,y2) and (x3,y3)
= 12(x1(y2y3)+x2(y3y1)+x3(y1y2)]


Area of the above shown triangle =12((5)(25)+(4)(56)+(7)(6(2))]
= 12(35+4+56)
= 47.5 square units.



By joining B to D, we get two triangles ABD and BCD.

Area of the Δ ABD = 12((5)(55)+(4)(57)+4(7+5)]
= 12(50+8+48)
= 53 square units

Area of the Δ BCD =12((4)(65)+(1)(5+5)+4(5+6)]
=12(4410+4)=19 square units

Therefore area of the quadrilateral ABCD = 53+19 = 72 square units

Note: To find the area of the polygon, divide it into triangles regions, which have no common area and add the areas of these regions


Area of the given above Δ ABC = 12(2(0+4)+(1)(43)+2(30)]
= 12(8+7+6)
= 10.5 square units

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