Question

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

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Answer 1

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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