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Find the area of polygon ABCDEF, if AD = 18cm, AQ =14 cm, AP = 12 cm, AN = 8 cm, AM = 4 cm, and FM, EP, QC and BN are perpendiculars to diagonal AD

Find the area of polygon ABCDEF, if AD = 18cm, AQ =14 cm, AP = 12 cm, AN = 8 cm, AM = 4 cm, and FM, EP, QC and BN are perpendiculars to diagonal AD

Solution:

The Figure above comprises the following shapes:

(1) △AFM with AM(Base) = 4 and FM(Altitude) = 5 cm

(2) △ANB with AN(base) = 8 cm and NB(Height) = 5cm

(3) Trapezium FMPE with parallel sides FM(5 cm) and PE(6 cm) and height PM = AP - AM = 12 - 4 = 8cm

(4) Trapezium BNQC with parallel sides NB(5 cm) and QC(4 cm) and height NQ = AQ - AN = 14 - 8 = 6 cm

(5) △EPD with PD(Base) = AD - AP = 18 - 12 = 6cm and height EP = 6cm

(6) △QCD with QD(Base) = AD - AQ = 18 - 14 = 4cm and height QC = 4 cm

Total Area = Area of △AFM + Area of △ANB + Area of Trapezium FMPE + Area of TrapeziumBNQC + Area of △EPD + Area of △QCD

Total Area = (½)(AM)(FM) + (½)(AN)(NB) + (½)(FM + PE)(PM) + + (½)(NB + QC)(NQ) + (½)(PD)(EP) + (½)(QD)(QC)

Total Area = (½)(4)(5) + (½)(8)(5) + (½)(5 + 6)(8) + (½)(5 + 4)(6) + (½)(6)(6) + (½)(4)(4)

Total Area = 10 + 20 + 44 + 27 + 18 + 8 = 127 cm²

✦Try This: Find the area of polygon ABCDEF, if AD = 20 cm, AQ =16 cm, AP = 14 cm, AN = 10 cm, AM = 6 cm, and FM, EP, QC and BN are perpendiculars to diagonal AD.

Find the area of polygon ABCDEF, if AD = 20 cm, AQ =16 cm, AP = 14 cm, AN = 10 cm, AM = 6 cm, and FM, EP, QC and BN are perpendiculars to diagonal AD.

The Figure above comprises the following shapes:

(1) △AFM with AM(Base) = 6 and FM(Altitude) = 7 cm

(2) △ANB with AN(base) = 10 cm and NB(Height) = 7cm

(3) Trapezium FMPE with parallel sides FM(7 cm) and PE(8 cm) and height PM = AP - AM = 14 - 6 = 8 cm

(4) Trapezium BNQC with parallel sides NB(7 cm) and QC(6 cm) and height NQ = AQ - AN = 16 - 10 = 6 cm

(5) △EPD with PD(Base) = AD - AP = 20 - 14 = 6cm and height EP = 8cm

(6) △QCD with QD(Base) = AD - AQ = 20 - 16 = 4cm and height QC = 6 cm

Total Area = Area of △AFM + Area of △ANB + Area of Trapezium FMPE + Area of TrapeziumBNQC + Area of △EPD + Area of △QCD

Total Area = (½)(AM)(FM) + (½)(AN)(NB) + (½)(FM + PE)(PM) + + (½)(NB + QC)(NQ) + (½)(PD)(EP) + (½)(QD)(QC)

Total Area = (½)(6)(7) + (½)(10)(7) + (½)(7 + 8)(8) + (½)(7 + 6)(8) + (½)(6)(8) + (½)(4)(6)

Total Area = 21 + 35 + 60 + 52 + 24 + 12 = 204 cm²

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Sample Problem 10

Find the area of polygon ABCDEF, if AD = 18cm, AQ =14 cm, AP = 12 cm, AN = 8 cm, AM = 4 cm, and FM, EP, QC and BN are perpendiculars to diagonal AD

Summary:

The area of polygon ABCDEF, if AD = 18cm, AQ =14 cm, AP = 12 cm, AN = 8 cm, AM = 4 cm, and FM, EP, QC and BN are perpendiculars to diagonal AD is 127 cm²

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