Plot the points A(7,0), B(2,5), C(7,5), D(5,3), E(2,3), F(2,-2), G(4,-4), H(-4,-4), I (-2,-2), J(-2,3), K(-5,3), L(-7,5), M(-2,5). Join them in order(A to B to C and so on)
Find the areas of the triangle ABM, Trapeziums (BCDE, FGHI, JKLM), and rectangle MBFI.
Hence find the total area of the figure so formed
Answers
Given : points A(0,7), B(2,5), C(7,5), D(5,3), E(2,3), F(2,-2), G(4,-4), H(-4,-4), I (-2,-2), J(-2,3), K(-5,3), L(-7,5), M(-2,5).
To find : areas of the triangle ABM, Trapeziums (BCDE, FGHI, JKLM), and rectangle MBFI.
Solution:
triangle ABM, BM is the base = 4 (= 2 -(-2)) Height = 2 = ( 7 - 5)
Area = (1/2)*4*2 = 4 sq units
Area of Trapeziums BCDE , BC = 5 DE = 3 , BE ( height) = 2
Area = (1/2)(5 + 3) * 2 = 8 sq units
Area of Trapeziums FGHI , FI = 4 GH = 8 , ( height) = 2
Area = (1/2)(4 + 8) * 2 = 12 sq units
Area of Trapeziums JKLM , JK = 3 LM = 5 , JM ( height) = 2
Area = (1/2)(5 + 3) * 2 = 8 sq units
rectangle MBFI. MB = 4 BF = 7
Area = 4 * 7 = 28 sq units
Total area = 4 + 8 + 12 + 8 + 28 = 60 sq units
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